Economic Principles in Agribusiness: Time Value of Money Time...Economic Principles in Agribusiness EP6 Time Value of Money Economic Principles in Agribusiness: Time Value of Money

Economic Principles in Agribusiness EP6 Time Value of Money

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Time value of money Interest Six Functions of the Dollar Future value of a dollar Rule of 72 Future value of a dollar per period Annuity


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Sinking fund factor Present value of the dollar Present value of a dollar per period Amortization


Economic Principles in Agribusiness: Time Value of Money EP6.1

Calculating the Six Functions of a Dollar

Future Value of a Dollar

If land is currently priced at $8000 per acre, what will the value of land be in five years with an

8% annual inflation rate? Assume that no other factor is affecting the value of land.

If you invested $100 in a savings account at 7% interest, how much money would you have in

40 years?

Rule of 72

How many years are required for $50 to double if it is earning 4% interest?

How many years will it require for $1,000 to double if earning 16% interest?

Future Value of an Annuity

Find the future value of a $5 annuity at 10% for five years.

Find the future value of a $7 annuity at 8% for three years.

Sinking Fund Factors

Joyce would like to buy a car following her college graduation after 4 more years of school. She

estimates the car will cost $ 10,000 when she graduates. If her savings account pays a 5% annual

rate of interest, compounded monthly, how much does she need to deposit monthly to have

$10,000 when she graduates in 4 years?



Present Value of the Dollar

A gentleman is investing in a savings bond. If the bond would be worth $50 when it matures at

the end of five years at 5%, what would it be worth today?

A timber buyer has offered to buy the timber in your woodlot for $13,000. After checking with

the farm forester, you find that the forester estimates that this stand would be worth $20,000 ten

years from now. If interest is 8%, should you sell now or wait 10 years? Assume there are

practically no costs associated with waiting 10 years.

Present Value of an Annuity

Jill’s parents will receive $10,000 per year in annual installments from an annuity for the next 20

years. If the fund provides a minimum annual return of 7% on the investments, what is the

present value of the annuity based on the minimum return?

Amortization

Jennifer plans to buy her first car and will need to borrow $5000. If she can get a 5 year, equal

amortized monthly payment loan with a 6% fixed interest rate, what will her monthly payments

be?


Economic Principles in Agribusiness: Time Value of Money EP6.1 KEY

Calculating the Six Functions of a Dollar


If land is currently priced at $8000 per acre, what will the value of land be in five years with an

8% annual inflation rate? Assume that no other factor is affecting the value of land.

𝐹𝑉 = 𝑃𝑉 𝑥 (1 + 𝑖)𝑛𝑡

𝐹𝑉 = 8000 𝑥 (1 + .08)5 = $11,755

If you invested $100 in a savings account at 7% interest, how much money would you have in

40 years?

𝐹𝑉 = 100 𝑥 (1 + .07)40 = $1,497.40

Rule of 72

How many years are required for $50 to double if it is earning 4% interest?

72/4 = 18 years

How many years will it require for $1,000 to double if earning 16% interest?

72/16 = 4.5 years

Future Value of an Annuity

Find the future value of a $5 annuity at 10% for five years.

Yr. 1 = $5 Yr. 2 = $5 + (5 x .10 = .5) + $5 = $10.50

Yr. 3 = $10.50 + (10.50 x .10) + $5 = $16.55 Yr. 4 = $16.55 + (16.55 x .10) + $5 = $23.21

Yr. 5 = $23.21 + (23.21 x .10) + $5 = $30.53

Find the future value of a $7 annuity at 8% for three years.

Yr. 1 = $7 Yr. 2 = $7 + (7 x .08) + $7 = $14.56 Yr. 3 = $14.56 + (14.56 x .08) + 7 = $22.72

Sinking Fund Factors

Joyce would like to buy a car following her college graduation after 4 more years of school. She

estimates the car will cost $10,000 when she graduates. If her savings account pays a 5% annual

rate of interest, compounded monthly, how much does she need to deposit monthly to have

$10,000 when she graduates in 4 years?

𝑃𝑀𝑇 = 𝐹𝑉 ∗

𝑖

𝑛

(1 + 𝑖

𝑛)

𝑛𝑡−1

𝑃𝑀𝑇 = 10,000 ∗

.05

12

(1 + .05

12)

(12)(4)−1

𝑃𝑀𝑇 = 10,000 𝑥 .004166667

(1.004166667)48−1

𝑃𝑀𝑇 = 41.66667

. 22089534 𝑃𝑀𝑇 = $188.63



Present Value of the Dollar

A gentleman is investing in a savings bond. If the bond would be worth $50 when it matures at

the end of five years at 5%, what would it be worth today?

𝑃𝑉 = 𝐹𝑉 𝑥 1

(1 + 𝑖)𝑛𝑡

𝑃𝑉 = 50 𝑥 1

(1+.05)5 = $39.17

A timber buyer has offered to buy the timber in your woodlot for $13,000. After checking with

the farm forester, you find that the forester estimates that this stand would be worth $20,000 ten

years from now. If interest is 8%, should you sell now or wait 10 years? Assume there are

practically no costs associated with waiting 10 years.

𝑃𝑉 = 𝐹𝑉 𝑥 1

(1 + 𝑖)𝑛𝑡

𝑃𝑉 = 20,000 𝑥 1

(1+.08)10 = $9263.87

Because the $20,000 has a present value of only $9264, the farmer would probably want to sell

the trees for $13,000.

Present Value of an Annuity

Jill’s parents will receive $10,000 per year in annual installments from an annuity for the next 20

years. If the fund provides a minimum annual return of 7% on the investments, what is the

present value of the annuity based on the minimum return?

𝑃𝑉 = 𝑃𝑀𝑇 [(1 +

𝑖

𝑛)

𝑛𝑡−1]

(1 + 𝑖

𝑛)

𝑛𝑡∗ (

𝑖

𝑛)

𝑃𝑉 = 10,000

[(1 + .07

1)

(1)(20)−1]

(1 + .07

1)

(1)(20)∗ (

.07

1)

𝑃𝑉 = 10,000 [(1.07)20−1]

(1.07)20∗ (.07)

𝑃𝑉 =10,000 [2.86968446]

0.270877912 𝑃𝑉 =

28696.8446

. 270877912 𝑃𝑉 = $105,940.14

Amortization

Jennifer plans to buy her first car and will need to borrow $5000. If she can get a 5 year, equal

amortized monthly payment loan with a 6% fixed interest rate, what will her monthly payments

be? 𝑃𝑀𝑇 = 𝑃𝑉 (

𝑖

𝑛)

1− (1 + 𝑖

𝑛)

− 𝑛𝑡 𝑃𝑀𝑇 =5,000 (

.06

12)

1− (1 + .06

12)

− (12)(5) 𝑃𝑀𝑇 = 5,000 (.005)

1− (1.005)− 60

𝑃𝑀𝑇 = 25.0

1 − 0.7413272196 𝑃𝑀𝑇 =

25

0.258672804 𝑃𝑀𝑇 = $96.66



Six Functions of a Dollar Formulas

1) Future Value of $ 1: 𝐹𝑉 = 𝑃𝑉(1 + 𝑖)𝑛𝑡

2) Future Value of $ 1 Per Period: 𝐹𝑉 = 𝑃𝑀𝑇 [(1 +

𝑖

𝑛)

𝑛𝑡−1

𝑖

𝑛

]

3) Sinking Funds Factor: 𝑃𝑀𝑇 = 𝐹𝑉 ∗

𝑖

𝑛

(1 + 𝑖

𝑛)

𝑛𝑡−1

4) Present Value of $ 1: 𝑃𝑉 = 𝐹𝑉

(1 + 𝑖

𝑛)

𝑛𝑡

5) Present Value of $ 1 Per Period: 𝑃𝑉 = 𝑃𝑀𝑇 [(1 +

𝑖

𝑛)

𝑛𝑡−1]

(1 + 𝑖

𝑛)

𝑛𝑡∗ (

𝑖

𝑛)

6) Amortization (Partial Payment): 𝑃𝑀𝑇 = 𝑃𝑉 (

𝑖

𝑛)

1− (1 + 𝑖

𝑛)

− 𝑛𝑡



Amortization Practice

1. Josh would like to purchase a pickup truck that will cost $20,000. He plans to put $3000

cash down and finance the balance on a 4 year, equal amortized annual installment note

at 6% interest. What will his annual payments be?

P = $ 17,000 loan ($ 20,000 - $ 3000 = PV)

i = 6%, or .06 (interest)

n = 1 (annual)

t = 4 years

PMT = $ ? Annual payment

2. John and Sue are looking to buy their dream home. They have the 20% down payment

but need to borrow $200,000. If they can get a 30 year, equal amortized monthly pay loan

with a 5.5% fixed interest rate, what will their monthly payments be?

P = $ 200,000 loan (PV)

i = 5.5%, or .055 (interest)

n = 12 (monthly)

t = 30 years

PMT = $ ? Monthly payment



3. Ethan purchased a new big screen TV at a cost of $3000. He financed the purchase on his

credit card. The credit card terms require 48 monthly payments at an interest rate of 18%.

Solve the following: a) What is Ethan’s monthly payment; and b) What is the total cost

of the TV with finance charges?

a. Solve for monthly payment:

P = $ 3,000 loan (amount financed)


n = 12 (monthly)

t = 4 years (48 months)


b. Solve for total cost of TV:

Total cost of TV and finance charges

= $

4. XYZ Corporation is trading equipment that has a net trade difference of $150,000. The

finance company is offering 7 year terms with equal amortized, semi-annual payments

and a 5.25% fixed interest rate. If they finance the $150,000 net trade difference, what

will the semi-annual payments be?

P = $ 150,000 loan (PV)

i = 5.25%, or .0525 (interest)

n = 2 (semi-annual)

t = 7 years

PMT = ? Semi-annual payment



Amortization Practice

1. Josh would like to purchase a pickup truck that will cost $20,000. He plans to put $3000

cash down and finance the balance on a 4 year, equal amortized annual installment note

at 6% interest. What will his annual payments be?

P = $ 17,000 loan ($ 20,000 - $ 3000 = PV)


n = 1 (annual)

t = 4 years

PMT = $ ? Annual payment

𝑃𝑀𝑇 = 𝑃𝑉 (

𝑖𝑛)

1 − (1 + 𝑖𝑛)

− 𝑛𝑡 𝑃𝑀𝑇 = 17,000 (

. 061 )

1 − (1 + . 06

1 )− (1)(4)

𝑃𝑀𝑇 = 17,000 (0.06)

1 − (1.06)− 4

𝑃𝑀𝑇 =1020

1 − 0.792093663 𝑃𝑀𝑇 =

1020

0.207906337 𝑃𝑀𝑇 = $4,906.06

2. John and Sue are looking to buy their dream home. They have the 20% down payment

but need to borrow $200,000. If they can get a 30 year, equal amortized monthly pay loan

with a 5.5% fixed interest rate, what will their monthly payments be?

P = $ 200,000 loan (PV)

i = 5.5%, or .055 (interest)

n = 12 (monthly)

t = 30 years


𝑃𝑀𝑇 = 200,000 (

. 05512 )

1 − (1 + . 055

12 )− (12)(30)

𝑃𝑀𝑇 =200,000 (0.004583333)

1 − (1.004583333)− 360

𝑃𝑀𝑇 = 916.66

1 − 0.192775275 𝑃𝑀𝑇 =

916.666

0.807224725 𝑃𝑀𝑇 = $1,135.58



3. Ethan purchased a new big screen TV at a cost of $3000. He financed the purchase on his

credit card. The credit card terms require 48 monthly payments at an interest rate of 18%.

Solve the following: a) What is Ethan’s monthly payment; and b) What is the total cost

of the TV with finance charges?

c. Solve for monthly payment:

P = $ 3,000 loan (amount financed)


n = 12 (monthly)

t = 4 years (48 months)


𝑃𝑀𝑇 = 3,000 (

. 1812 )

1 − (1 + . 1812 )

−(12)(4) 𝑃𝑀𝑇 =

3,000 (0.015)

1 − 1.015)− 48 𝑃𝑀𝑇 =

45

1 − 0.48936169

𝑃𝑀𝑇 = $88.13

d. Solve for total cost of TV:

Total cost of TV and finance charges

= $ 88.13 x 48 = $4230.24

4. XYZ Corporation is trading equipment that has a net trade difference of $150,000. The

finance company is offering 7 year terms with equal amortized, semi-annual payments

and a 5.25% fixed interest rate. If they finance the $150,000 net trade difference, what

will the semi-annual payments be?

P = $ 150,000 loan (PV)

i = 5.25%, or .0525 (interest)

n = 2 (semi-annual)

t = 7 years


𝑃𝑀𝑇 = 150,000 (

. 05252 )

1 − (1 + . 0525

2 )−(2)(7)

𝑃𝑀𝑇 = 3,000 (0.02625)

1 − (1.02625)−14 𝑃𝑀𝑇 =

3.937.5

1 − 0.69575385

𝑃𝑀𝑇 = 3937.5

0.30424615 𝑃𝑀𝑇 = $12,941.82



Future Value of a Dollar Per Period Practice

1. Linda decides she would like to save $100 per month from her job to use towards buying

a used car when she graduates in 4 years. If she deposits $100 per month into her savings

account that pays 6% interest, compounded monthly, how much will she have at the end

of 4 years?

Pmt = $ 100 payment

i = 6%, or .06 Interest

n = 12 (monthly)

t = 4 years

FV = $ ? Future Value at end of 4 years

2. John recently graduated from college and has secured a good job in a career of his choice.

He decides to invest $600 per month in an investment that guarantees a 5.25% nominal rate

of interest, compounded monthly, over 20 years. What is the future value of his account at

the end of 20 years?

Pmt = $ 600 payment

i = 5.25%, or .0525 Interest

n = 12 (monthly)

t = 20 years

FV = $ ? Future Value in 20 years



3. Sara’s parents started her college fund when she was 6 years old. They deposited $500

per month and plan to continue to deposit this amount until she graduates school just

before her 19th birthday. If her parents continue to deposit the same payment into this

fund for 12 years that pays a 6% annual rate of interest, compounded monthly, how much

will Sara have in her college fund at the end of the 12 year investment period?

Pmt = $ 500 payment


n = 12 (monthly)

t = 12 years

FV = $ ? Future Value end of 12 years

4. An investor owns 200 acres of farmland. After all expenses are paid, the investor

determines she can place $25,000 per year in an investment account that pays 7%,

compounded annually. What is the expected future value of the investment account at the

end of 10 years?

Pmt = $ 25,000 payment


n = 1 (annual)

t = 10 years




Future Value of a Dollar Per Period Practice

1. Linda decides she would like to save $100 per month from her job to use towards buying

a used car when she graduates in 4 years. If she deposits $100 per month into her savings

account that pays 6%, compounded monthly, how much will she have at the end of 4

years?

Pmt = $ 100 payment

i = 6%, or .06

n = 12 (monthly)

t = 4 years


𝐹𝑉 = 𝑃𝑀𝑇 [(1 +

𝑖𝑛

)𝑛𝑡

− 1

𝑖𝑛

] 𝐹𝑉 = 100 [(1 +

. 0612

)(12)(4)

− 1

. 0612

]

𝐹𝑉 = 100 [(1.005)48 − 1

0.005] 𝐹𝑉 = 100 [

0.27048916

0.005 ] 𝐹𝑉 = 100[54.097832]

𝐹𝑉 = $5,409.78

2. John recently graduated from college and has secured a good job in a career of his choice.

He decides to invest $600 per month in an investment that guarantees a 5.25% nominal rate,

compounded monthly, over 20 years. What is the future value of his account at the end of

20 years?

Pmt = $ 600 payment

i = 5.25%, or .0525

n = 12 (monthly)

t = 20 years


𝐹𝑉 = 600 [(1 +

. 052512 )

(12)(20)

− 1

. 052512

] 𝐹𝑉 = 600 [(1.004375)240 − 1

0.004375]

𝐹𝑉 = 600 [2.851114 − 1

0.004375 ] 𝐹𝑉 = 600 [

1.851114

0.004375] 𝐹𝑉 = 600[423.11177]

𝐹𝑉 = $253,867.06



3. Sara’s parents started her college fund when she was 6 years old. They deposited $500

per month and plan to continue to deposit this amount until she graduates school just

before her 19th birthday. If her parents continue to deposit the same payment into this

fund for 12 years that pays a 6% annual rate, compounded monthly, how much will Sara

have in her college fund at the end of the 12 year investment period?

Pmt = $ 500 payment

i = 6%, or .06

n = 12 (monthly)

t = 12 years

FV = $ ? Future Value end of 12 years

𝐹𝑉 = 500 [(1 +

. 0612 )

(12)(12)

− 1

. 0612

] 𝐹𝑉 = 500 [(1.005)144 − 1

0.005]

𝐹𝑉 = 500 [2.0507508 − 1

0.005] 𝐹𝑉 = 500 [

1.0507508

0.005] 𝐹𝑉 = 500[210.150163]

𝐹𝑉 = $105,075.08

4. An investor owns 200 acres of farmland. After all expenses are paid, the investor

determines she can place $25,000 per year in an investment account that pays 7%,

compounded annually. What is the expected future value of the investment account at the

end of 10 years?


i = 7%, or .07

n = 1 (annual)

t = 10 years


𝐹𝑉 = 25,000 [(1 +

. 071 )

(1)(10)

− 1

. 071

] 𝐹𝑉 = 25,000 [(1 .07)10 − 1

0.07]

𝐹𝑉 = 25,000 [1.967151357 − 1

0.07] 𝐹𝑉 = 25,000 [

0.967151357

0.07]

𝐹𝑉 = 25,000[13.81644796] 𝐹𝑉 = $345,411.20



Future Value of a Dollar Practice

1. Jill receives a $5000 gift on her 16th birthday. She decides to invest it in a 5- year

certificate of deposit that pays a 5% nominal interest rate, compounded semi-annually.

What is the future value of this investment at its maturity?

PV = $ 5000 Initial Investment


n = 2 (semi-annual)

t = 5 years

FV = $ ? Future Value at maturity

2. A couple desires to purchase a house during a depressed market, believing it represents

an opportunity to a take advantage of low interest rates and expected real estate

appreciation. If the house costs $75,000 today and they anticipate a 6% annual

appreciation rate, what is the expected future value of the house at the end of 10 years?

PV = $ 75,000 Initial Investment

i = 6%, or .06 (appreciation rate)

n = 1 (annual)

t = 10 years




3. Kevin receives a $30,000 gift from his grandparents’ estate and decides to invest in a

savings account for future retirement. If the account pays an annual rate of 4% interest,

compounded monthly, what would the future value of this account be at the end of 30

years?

PV = $ 30,000 Initial Deposit


n = 12 (monthly)

t = 30 years


4. Nathan locates a 200-acre farm that has a value of $800,000 ($4000 per acre). What is the

expected future value at the end of 5 years assuming a 7% annual rate of appreciation?

PV = $ 800,000 Initial value


n = 1 (annual)

t = 5 years




Future Value of a Dollar Practice

1. Jill receives a $5000 gift on her 16th birthday. She decides to invest it in a 5- year

certificate of deposit that pays a 5% nominal interest rate, compounded semi-annually.

What is the future value of this investment at its maturity?

PV = $ 5000 Initial Investment


n = 2 (semi-annual)

t = 5 years

FV = $ ? Future Value at maturity

𝐹𝑉 = 𝑃𝑉 (1 + 𝑖

𝑛)

𝑛𝑡

𝐹𝑉 = 5,000 (1 + . 05

2)

(2)(5)

𝐹𝑉 = 5,000(1.025)10

𝐹𝑉 = 5,000 𝑋 1.28008454 𝐹𝑉 = $6,400.42

2. A couple desires to purchase a house during a depressed market, believing it represents

an opportunity to a take advantage of low interest rates and expected real estate

appreciation. If the house costs $75,000 today and they anticipate a 6% annual

appreciation rate, what is the expected future value of the house at the end of 10 years?

PV = $ 75,000 Initial Investment


n = 1 (annual)

t = 10 years


𝐹𝑉 = 75,000 (1 + . 06

1)

(1)(10)

𝐹𝑉 = 75,000(1.06)10 𝐹𝑉 = 75,000 𝑋 1.79084769

𝐹𝑉 = $134,313.58



3. Kevin receives a $30,000 gift from his grandparents’ estate and decides to invest in a

savings account for future retirement. If the account pays an annual rate of 4% interest,

compounded monthly, what would the future value of this account be at the end of 30

years?

PV = $ 30,000 Initial Deposit


n = 12 (monthly)

t = 30 years


𝐹𝑉 = 30,000 (1 + . 04

12)

(12)(30)

𝐹𝑉 = 30,000(1.003333333)360

𝐹𝑉 = 30,000 𝑋 3.313498014 𝐹𝑉 = $99,404.94

4. Nathan locates a 200-acre farm that has a value of $800,000 ($4000 per acre). What is the

expected future value at the end of 5 years assuming a 7% annual rate of appreciation?



n = 1 (annual)

t = 5 years


𝐹𝑉 = 800,000 (1 + . 07

1)

(1)(5)

𝐹𝑉 = 800,000(1.07)5 𝐹𝑉 = 800,000 𝑋 1.402551731

𝐹𝑉 = $1,122,041.39



Present Value of a Dollar Practice

1. Jill recently received a $50,000 gift from her grandmother’s estate. She would like to set

aside a portion of this gift into two accounts. The first account needs a lump sum deposit

in a sufficient amount to grow with compound interest to $15,000 when she graduates

from college in 6 years to buy a car. The second account needs a deposit in a sufficient

amount that will grow with interest to $40,000 for the same time period. She plans to use

this account for a down payment on a house. If both investments are invested for 6 years

that pay a 6% nominal rate of interest, compounded monthly, how much does she need to

deposit into each account to accumulate the desired amount for each?

a) Problem for Car:

FV = $ 15,000 Value at maturity

i = 6 %, or .06 rate

n = 12 (monthly)

t = 6 years

PV = $ ? Required deposit

b) Problem for down payment:


i = 6%, or .06 interest rate

n = 12 (monthly)

t = 6 years




2. You have set a goal to remodel and replace the roof on your house in 5 years with

expected costs to be $20,000 at that time. How much do you need to deposit today into an

investment account that pays 5% nominal rate of interest, compounded monthly, to meet

the $20,000 cost at the end of 5 years?

Formula:

FV = $20,000 Value at maturity

i = 5 %, or .05 rate

n = 12 (monthly)

t = 5 years


3. Your business will need $400,000 in 5 years to purchase a new piece of equipment. How

much do you need to deposit today into an investment account if the interest rate pays a

nominal rate of 5.75%, compounded semi-annually for 5 years, to have the $400,000

when needed?

FV = $ 400,000 Future Value equip cost

i = 5.75 %, or .0575 rate

n = 2 (semi-annual)

t = 5 years




Present Value of a Dollar Practice

1. Jill recently received a $50,000 gift from her grandmother’s estate. She would like to set

aside a portion of this gift into two accounts. The first account needs a lump sum deposit

in a sufficient amount to grow with compound interest to $15,000 when she graduates

from college in 6 years to buy a car. The second account needs a deposit in a sufficient

amount that will grow with interest to $40,000 for the same time period. She plans to use

this account for a down payment on a house. If both investments are invested for 6 years

that pay a 6% nominal rate of interest, compounded monthly, how much does she need to

deposit into each account to accumulate the desired amount for each?

c) Problem for Car:


i = 6 %, or .06 rate

n = 12 (monthly)

t = 6 years


𝑃𝑉 = 𝐹𝑉

(1 + 𝑖𝑛)

𝑛𝑡 𝑃𝑉 = 15,000

(1 + . 0612 )

(12)(6) 𝑃𝑉 =

15,000

(1.005)72 𝑃𝑉 =

15,000

1.432044278

𝑃𝑉 = $10,474.54

d) Problem for down payment:


i = 6%, or .06 interest rate

n = 12 (monthly)

t = 6 years


𝑃𝑉 = 40,000

(1 + . 0612 )

(12)(6) 𝑃𝑉 =

40,000

(1.005)72 𝑃𝑉 =

40,000

1.432044279 𝑃𝑉 = $27,932.10



2. You have set a goal to remodel and replace the roof on your house in 5 years with

expected costs to be $20,000 at that time. How much do you need to deposit today into an

investment account that pays 5% nominal rate of interest, compounded monthly, to meet

the $20,000 cost at the end of 5 years?

Formula:

FV = $20,000 Value at maturity

i = 5 %, or .05 rate

n = 12 (monthly)

t = 5 years


𝑃𝑉 = 20,000

(1 + . 0512 )

(12)(5) 𝑃𝑉 =

20,000

(1.004166667)60 𝑃𝑉 =

20,000

1.283358678 𝑃𝑉 = $15,584.11

3. Your business will need $400,000 in 5 years to purchase a new piece of equipment. How

much do you need to deposit today into an investment account if the interest rate pays a

nominal rate of 5.75%, compounded semi-annually for 5 years, to have the $400,000

when needed?

FV = $ 400,000 Future Value equip cost

i = 5.75 %, or .0575 rate

n = 2 (semi-annual)

t = 5 years


𝑃𝑉 = 400,000

(1 + . 0575

2 )(2)(5)

𝑃𝑉 =400,000

(1.02875)10 𝑃𝑉 =

400,000

1.327695497 𝑃𝑉 = $301,273.90



Present Value of a Dollar Per Period Practice

1. A young couple buys their first house with owner financing. Their payments are $1000

per month for 15 years with a 5% fixed interest rate. The note holder would like to sell

the note to an investor. What would be the discounted present value of the note

receivable with 15 years of payments remaining?

a) Solve for present value of the note.

PMT = $ 1,000 per period

i = 5%, or .05 interest

n = 12 (monthly)

t = 15 years

PV = $ ? Solve for Present Value

b) If the monthly payments to maturity of the note total $180,000 ($1000 per mo. x 180

payments), what is the dollar amount of the discount if the note is sold to the

investor?

Total value of 180 Payments = $

Less Present Value (answer from a.) - $_____________

Total amount of discount = $



2. Jack is considering a purchase of rental investment property that generates $10,000 net

cash flow after all expenses and taxes are paid. If this income is expected over the next 20

years and the desired annual rate of return is 8%, what is the present value today of this

rental property based on the net after tax cash flow?



n = 1 (annual)

t = 20 years

PV = $ ? Present Value of Rental property

3. A land contract pays $50,000 per year with annual installments on March 1st for the next

10 years. If the expected annual rate of return is 6%, what is the present value of this

contract?



n = 1 (annual)

t = 10 years

PV = $ ? Present Value of 10 yr. contract



4. An investor considers an investment that has a guaranteed annual net cash flow after

expenses of $12,500 per year for the next ten years. If the investor desires a 10% return

per year on the investment, what would current value today be for the 10 year cash flow?

a) Solve for today’s value of 10 year cash flow:

PMT = $ 12,500 payment


n = 1 (annual)

t = 10 years

PV = $ Today’s current Value

b) Solve for today’s value of the 10 year cash flow with a 5% rate of return:

Use the same investment and same annual net cash flow with a current value with a 5%

return:


i = 5%, or .05% interest

n = 1 (annual)

t = 10 years

PV = $ ? Today’s current value



Present Value of a Dollar Per Period Practice

1. A young couple buys their first house with owner financing. Their payments are $1000

per month for 15 years with a 5% fixed interest rate. The note holder would like to sell

the note to an investor. What would be the discounted present value of the note

receivable with 15 years of payments remaining?

c) Solve for present value of the note.



n = 12 (monthly)

t = 15 years

PV = $ ? Solve for Present Value

𝑃𝑉 = 𝑃𝑀𝑇 [(1 +

𝑖𝑛)

𝑛𝑡

− 1]

(1 + 𝑖𝑛)

𝑛𝑡

∗ (𝑖𝑛)

𝑃𝑉 = 1,000

[(1 + . 0512 )

(12)(15)

− 1]

(1 + . 0512 )

(12)(15)

∗ (. 0512 )

𝑃𝑉 =1,000 [(1.004166667)180 − 1]

(1.004166667)180 ∗ (. 004166667) 𝑃𝑉 =

1,000 [1.113704059]

2.113704059 ∗ .00416666

𝑃𝑉 =1113.704059

0.008807101 𝑃𝑉 = $126,455.21

d) If the monthly payments to maturity of the note total $180,000 ($1000 per mo. x 180

payments), what is the dollar amount of the discount if the note is sold to the

investor?

Total value of 180 Payments = $ 180,000 = 1,000 x 180 payments

Less Present Value (answer from a.) - $__126,455___________

Total amount of discount = $ 53,545



2. Jack is considering a purchase of rental investment property that generates $10,000 net

cash flow after all expenses and taxes are paid. If this income is expected over the next 20

years and the desired annual rate of return is 8%, what is the present value today of this

rental property based on the net after tax cash flow?



n = 1 (annual)

t = 20 years

PV = $ ? Present Value of Rental property

𝑃𝑉 = 10,000

[(1 + . 08

1 )(1)(20)

− 1]

(1 + . 08

1 )(1)(20)

∗ (. 08

1 )

𝑃𝑉 = 10,000 [(1.08)20 − 1]

(1.08)20 ∗ (0.08)

𝑃𝑉 = 10,000 [3.660957144]

4.6600957144 ∗ 0.08 𝑃𝑉 =

36609.57144

0.37287657 𝑃𝑉 = $98,181.47

3. A land contract pays $50,000 per year with annual installments on March 1st for the next

10 years. If the expected annual rate of return is 6%, what is the present value of this

contract?



n = 1 (annual)

t = 10 years

PV = $ ? Present Value of 10 yr. contract

𝑃𝑉 = 50,000

[(1 + . 06

1 )(1)(10)

− 1]

(1 + . 06

1 )(1)(10)

∗ (. 06

1 )

𝑃𝑉 = 50,000 [(1.06)10 − 1]

(1.06)10 ∗ (0.06)

𝑃𝑉 = 50,000 [0.790847697]

1.790847697 ∗ 0.06 𝑃𝑉 =

39542.38

0.10745 𝑃𝑉 = $368,008.26



4. An investor considers an investment that has a guaranteed annual net cash flow after

expenses of $12,500 per year for the next ten years. If the investor desires a 10% return

per year on the investment, what would current value today be for the 10 year cash flow?

c) Solve for today’s value of 10 year cash flow:



n = 1 (annual)

t = 10 years

PV = $ Today’s current Value

𝑃𝑉 = 12,500

[(1 + . 10

1 )(1)(10)

− 1]

(1 + . 10

1 )(1)(10)

∗ (. 10

1 )

𝑃𝑉 = 12,500 [(1.10)10 − 1]

(1.10)10 ∗ (0.10)

𝑃𝑉 = 12,500 [1.59374246]

0.259374246 𝑃𝑉 =

19921.78075

0.259374246 𝑃𝑉 = $76,807.09

d) Solve for today’s value of the 10 year cash flow with a 5% rate of return:

Use the same investment and same annual net cash flow with a current value with a 5%

return:


i = 5%, or .05% interest

n = 1 (annual)

t = 10 years

PV = $ ? Today’s current value

𝑃𝑃𝑉 = 12,500

[(1 + . 05

1 )(1)(10)

− 1]

(1 + . 05

1 )(1)(10)

∗ (. 05

1 )

𝑃𝑉 = 12,500 [(1.05)10 − 1]

(1.05)10 ∗ (0.05)

𝑃𝑉 = 12,500 [0.628894627]

0.081444731 𝑃𝑉 =

7861.18

0.081444731 𝑃𝑉 = $96,521.65



Sinking Funds Factor Practice

1. A young couple plans to buy a house at the end of 10 years and will need $20,000 for

their cash down payment. If they can invest in a fund that pays an annual rate of 6%

interest, compounded quarterly, how much do they need to invest quarterly to have

$20,000 at the end of 10 years?

FV = $ 20,000 Future Value 10 years


n = 4 (quarterly)

t = 10 years

Pmt = $ ? Quarterly deposit

2. Jill would like to expand her business in 5 years. She estimates the cost to be $75,000 at

the time of expansion and plans to make quarterly deposits to an investment fund. If the

fund pays a 7% annual return, compounded quarterly, how much does she need to invest

quarterly to have $75,000 at the end of 5 years?

FV = $ 75,000 Future Value in 5 years


n = 4 (quarterly)

t = 5 years




3. A young couple has an opportunity to take over a neighbor’s farm operation in 7 years

due to the neighbor’s planned retirement. They also plan to purchase his line of

equipment that will have an estimated value of $200,000 at that time. How much will

they need to deposit annually into an investment account if the account pays a 4%

nominal rate of interest, compounded annually, to have the $200,000 needed at the end of

7 years?

FV = $ 200,000 Value needed in 7 years


n = 1 (annual)

t = 7 years

Pmt = $ ? Annual deposit

4. Jack has a seed cleaning business in addition to his farming operation. He would like it to

stand on its own and meet its ongoing equipment replacement needs. If equipment

replacement costs $75,000 every 5 years, how much does he need to invest monthly into

a money market account if it pays 5% interest, compounded monthly, to meet the

$75,000 future capital purchase requirement?

FV = $ 75,000 (Future Value Equip Cost)


n = 12 (monthly)

t = 5 years

Pmt = $ ? Monthly deposit



Sinking Funds Factor Practice

1. A young couple plans to buy a house at the end of 10 years and will need $20,000 for

their cash down payment. If they can invest in a fund that pays an annual rate of 6%

interest, compounded quarterly, how much do they need to invest quarterly to have

$20,000 at the end of 10 years?

FV = $ 20,000 Future Value 10 years


n = 4 (quarterly)

t = 10 years


𝑃𝑀𝑇 = 𝐹𝑉 ∗

𝑖𝑛

(1 + 𝑖𝑛)

𝑛𝑡

− 1

𝑃𝑀𝑇 = 20,000 ∗

. 064

(1 + . 06

4 )(4)(10)

− 1

𝑃𝑀𝑇 = 20,000 ∗ 0.015

(1.015)40 − 1

𝑃𝑀𝑇 = 300

0.8140184𝑃𝑀𝑇 = $368.54

2. Jill would like to expand her business in 5 years. She estimates the cost to be $75,000 at

the time of expansion and plans to make quarterly deposits to an investment fund. If the

fund pays a 7% annual return, compounded quarterly, how much does she need to invest

quarterly to have $75,000 at the end of 5 years?

FV = $ 75,000 Future Value in 5 years


n = 4 (quarterly)

t = 5 years


𝑃𝑀𝑇 = 75,000 ∗

. 074

(1 + . 07

4 )(4)(5)

− 1

𝑃𝑀𝑇 = 75,000 ∗ 0.0175

(1.0175)20 − 1𝑃𝑀𝑇 =

1312.5

0.414778196

𝑃𝑀𝑇 = $3,164.34



3. A young couple has an opportunity to take over a neighbor’s farm operation in 7 years

due to the neighbor’s planned retirement. They also plan to purchase his line of

equipment that will have an estimated value of $200,000 at that time. How much will

they need to deposit annually into an investment account if the account pays a 4 %

nominal rate of interest, compounded annually, to have the $200,000 needed at the end of

7 years?

FV = $ 200,000 Value needed in 7 years


n = 1 (annual)

t = 7 years

Pmt = $ ? Annual deposit

𝑃𝑀𝑇 = 200,000 ∗

. 041

(1 + . 04

1 )(1)(7)

− 1

𝑃𝑀𝑇 = 200,000 ∗ 0.04

(1.04)7 − 1𝑃𝑀𝑇 =

8,000

0.315931779

𝑃𝑀𝑇 = $25,321.92

4. Jack has a seed cleaning business in addition to his farming operation. He would like it to

stand on its own and meet its ongoing equipment replacement needs. If equipment

replacement costs $75,000 every 5 years, how much does he need to invest monthly into

a money market account if it pays 5% interest, compounded monthly, to meet the

$75,000 future capital purchase requirement?

FV = $ 75,000 (Future Value Equip Cost)


n = 12 (monthly)

t = 5 years

Pmt = $ ? Monthly deposit

𝑃𝑀𝑇 = 75,000 ∗

. 0512

(1 + . 0512 )

(12)(5)

− 1

𝑃𝑀𝑇 = 75,000 ∗

0.004166667𝑛

(1.004166667)60 − 1

𝑃𝑀𝑇 =312.50

0.283358704𝑃𝑀𝑇 = $1,102.84



Time Value of Money Blog Evaluation

Locate three articles pertaining to time value of money, discounting, compounding, interest,

inflation, etc. Use MSN Money, CNN Money, or Yahoo Money to begin your search.

After reading and taking notes over all three articles, write a blog post about the key information

in the articles. Include how you feel about the information, tips shared in the article, and how

you plan to use the information in your own life.

Once all student blog posts are complete, each student will be assigned two blog posts with

which to read and respond in a short blog comment. This response should pertain to an

agreement of the blog post, an opposition of the blog post, personal past experiences pertaining

to the blog post, and/or how they personally might use this information in his/her life. Blog

comments simply stating, “I agree,” “I disagree,” “Good point,” etc. will not be accepted. Blog

comments must recall information learned from reading the initial blog post.



Insurance Blog Evaluation Rubric

20 points 15 points 10 points 5 points

Con

ten

t

Blog post provides

comprehensive insight,

clear understanding, and

reflective thought about

the topic. It builds a

focused argument

around the issue, poses

questions to the reader,

and/or makes an

opposing statement

supported by personal

experiences.

Blog post provides

moderate insight,

clear understanding,

and reflective

thought about the

topic.

Blog post

provides

minimal insight,

understanding,

and reflective

thought about

the topic.

Blog post lacks

insight,

understanding

and reflective

thought about

the topic.

Vie

wp

oin

t C

reate

d Blog post presents a

focused viewpoint

supported by examples

from articles read and

content learned in lesson

to enhance blog

viewpoint.

Blog post presents a

focused viewpoint

supported by

examples from

articles read and

content learned in

lesson, but does not

enhance blog

viewpoint.

Blog post

presents a

focused

viewpoint, but

is not supported

by articles or

content from

lesson.

Blog post lacks

a focused

viewpoint.

Cre

ati

vit

y i

n

Wri

tin

g

Blog post is creatively

written and easily

stimulates dialogue and

comments.

Blog post is

creatively written

and can somewhat

stimulate dialogue

and comments.

Blog post is

brief and

unimaginative,

lacking the

ability to easily

connect with

readers.

Blog post does

not stimulate

dialogue and

comments.

Cit

ati

on

s

Quotations and

comments directly from

articles are used

effectively and cited

correctly.

Quotations and

comments directly

from articles

somewhat enhance

the blog post and

are cited correctly.

Quotations and

comments

directly from

articles do not

enhance blog

post and/or are

cited

incorrectly.

Quotations and

comments

directly from

articles are not

used in blog

post.

Qu

ali

ty o

f

Wri

tin

g

Writing is free of

grammatical, spelling,

and punctuation errors.

Writing has 1-2

grammatical,

spelling, or

punctuation errors.

Writing has 3-4

grammatical,

spelling, or

punctuation

errors.

Writing has 5

or more

grammatical,

spelling, or

punctuation

errors.



Time Value of Money Alternative Evaluation

Amortization

1. A company is purchasing $500,000 of new equipment and has offered additional equity

to the lender to secure the finance request. Loan approval terms call for 10 year, equal

amortized, quarterly payments at a 6.25% fixed rate of interest. What will the quarterly

payments be?

P = $ 500,000 loan (PV)

i = 6.25%, or .0625 (interest)

n = 4 (quarterly)

t = 10 years

PMT = $ ? Quarterly payment

2. High Profit Farms, LLC just closed on a new $5,000,000 real estate mortgage secured by

2,000 acres. The new loan repayment terms are on 25 year, equal amortized, semi-annual

installments with interest fixed at a rate of 5.2%. What are the semi-annual payments for

this new mortgage note?

P = $ 5,000,000 loan (PV)

i = 5.20%, or .0520 (interest)

n = 2 (semi-annual)

t = 25 years




Future Value of a Dollar Per Period

3. Courtney and her husband recently graduated from college. Both have excellent paying

jobs in the city, but they would like to move back to the farm and take over their parents’

farm operation when they retire. They plan to live on Courtney’s salary for the next 10

years and invest her husband’s $ 4,000 per month net pay into an investment savings

account. If the account earns 5% interest, compounded monthly, what is the expected

future value of their account at the end of 10 years?



n = 12 (monthly)

t = 10 years


4. A business determines it will need to replace equipment in 5 years. The business plan

calls for $2500 per month deposits into a capital savings account that pays a 6% rate

annual rate of interest, compounded monthly. What is the future value of the capital

account at the end of 5 years?



n = 12 (monthly)

t = 5 years





5. Joe decides to buy land as a hedge against inflation. He finds 100 acres for sale at $3000

per acre. Land values in this area consistently appreciate at an annual rate of 4%. If Joe

buys the property for $3000 per acre, what is the future value per acre at the end of 15

years, assuming a 4% annual appreciation rate?

PV = $ 3,000 per acre ( Initial value)


n = 1 (annual)

t = 15 years

FV = $ ? Future Value per acre

6. A young business owner is preparing his 5 year business plan and is trying to determine

the impact of a 3% annual inflation rate to his operating expenses over the next 5 year

period. If his first years operating expense is $200,000, what is the expected operating

expense projection at the end of 5 years, assuming all expense inputs remain the same?



n = 1 (annual)

t = 5 years

FV = $ ? Projected expense end of year 5



Present Value of a Dollar

7. Jill would like to buy a 15 year bond today that has a face value of $30,000 at its

maturity. If the bond pays 4.5%, compounded monthly, what is expected present value of

the bond?

FV = $ 30,000

i = 4.5 %, or .045 rate

n = 12 (monthly)

t = 15 years

PV = $ ? Present Value of bond

8. Calculate the present value (purchase price) of a property that is expected to be sold for

$400,000 in 5 years, assuming an annual appreciation rate of 4%.

Formula:

FV = $ 400,000

i = 4 %, or .04 rate

n = 1 (annual)

t = 5 years

PV = $ ? Present Value of Property



Present Value of a Dollar Per Period

9. The company you worked for the past 25 years plans to downsize operations and will

offer qualified employees early retirement packages. They offer you a choice of a) 20

years of equal monthly annuity payments of $2500 per month that guarantees a 4%

minimum return on the annuity investments; or b) a lump sum cash settlement of

$375,000. In this problem, you will determine a) the present value of the annuity (PV)

payments and b) which option provides the largest present value (PV).

a) Solve for present value of the annuity:

PMT = $ 2500 (payment)


n = 12 (monthly)

t = 20 years

PV = $ ? Present Value of Annuity

b) Calculate the difference between the cash settlement and present value of the annuity.

Which is higher?

PV of Annuity (from part a) = $ ?

Cash settlement = $ 375,000

Net Difference = $



Sinking Funds Factor

10. A young couple wants to buy 100 acres at the end of their first 10 years of farming and

wants to save enough funds for a 35% cash down payment. If the 100 acres will cost

$5000 per acre in 10 years, how much will they need for their 35% down payment? In

addition, how much do they need to invest semi-annually in an investment account to

then have the down payment amount if the account pays 3.75% annual rate of interest,

compounded semi-annually?

Problems:

a. How much down payment will be needed in 10 years (Future Value)?

b. What is the semi-annual deposit required to meet the 35% cash down payment

needed in 10 years?

FV = $ ? (Answer from a. for down payment)

i = 3.75%, or .0375 interest rate

n = 2 (semi - annual)

t = 10 years

Pmt = $ ? Semi-Annual deposit



11. A young couple wants to buy their parents’ trucking business at the conclusion of the

next 3 years to coincide with their parents’ retirement. The operation consists of 4 over

the road tractor trailer units, and the parents have agreed to sell them at the end of 3 years

for $ 25,000 each.

Problems:

a. How much is needed to complete the purchase at the end of 3 years?

b. How much will the couple need to invest into their savings account quarterly if

interest is compounded quarterly with a 4.75% nominal rate of interest to

complete this purchase?

FV = $ ? (From a. above Future Value)


n = 4 (quarterly)

t = 3 years



Time Value of Money Alternative Evaluation

Amortization

1. A company is purchasing $500,000 of new equipment and has offered additional equity

to the lender to secure the finance request. Loan approval terms call for 10 year, equal

amortized, quarterly payments at a 6.25% fixed rate of interest. What will the quarterly

payments be?

P = $ 500,000 loan (PV)

i = 6.25%, or .0625 (interest)

n = 4 (quarterly)

t = 10 years

PMT = $ ? Quarterly payment

PMT = PV (

in)

1 − (1 + in)

− nt PMT = 500,000 (

. 06254 )

1 − (1 + . 0625

4 )− (4)(10)

PMT = 500,000 (0.015625)

1 − (1.015625)− 40

PMT = 7812.5

1 − 0.53785436 PMT =

7812.5

0.46214564 PMT = $16,904.84

2. High Profit Farms, LLC just closed on a new $5,000,000 real estate mortgage secured by

2,000 acres. The new loan repayment terms are on 25 year, equal amortized, semi-annual

installments with interest fixed at a rate of 5.2%. What are the semi-annual payments for

this new mortgage note?

P = $ 5,000,000 loan (PV)

i = 5.20%, or .0520 (interest)

n = 2 (semi-annual)

t = 25 years


PMT = PV (

in)

1 − (1 + in)

− nt PMT = 5,000,000 (

. 0522 )

1 − (1 + . 052

2 )− (2)(25)

PMT = 130,000

1 − 0.277097088

PMT = 130,000

0.722902912 PMT = $179,830.51



Future Value of a Dollar Per Period

3. Courtney and her husband recently graduated from college. Both have excellent paying

jobs in the city, but they would like to move back to the farm and take over their parents’

farm operation when they retire. They plan to live on Courtney’s salary for the next 10

years and invest her husband’s $4,000 per month net pay into an investment savings

account. If the account earns 5% interest, compounded monthly, what is the expected

future value of their account at the end of 10 years?



n = 12 (monthly)

t = 10 years


FV = PMT [(1 +

in)

nt

− 1

in

] FV = 4,000 [(1 +

. 0512 )

(12)(10)

− 1

. 0512

]

FV = 4,000 [(1.004166667)120 − 1

0.004166667] FV = 4,000 [

1.647009498 − 1

0.004166667]

FV = 4,000 [0.647009498

0.004166667] FV = 4,000[155.2822671] FV = $621,129.13

4. A business determines it will need to replace equipment in 5 years. The business plan

calls for $2500 per month deposits into a capital savings account that pays a 6% rate

annual rate of interest, compounded monthly. What is the future value of the capital

account at the end of 5 years?



n = 12 (monthly)

t = 5 years


FV = 2,500 [(1 +

. 0612 )

(12)(5)

− 1

. 0612

] FV = 2,500 [(1.005)60 − 1

0.005]

FV = 2,500 [1.348850 − 1

0.005] FV = 2,500 [

0.3488501

0.005] FV = 2,500[69.77002]

FV = $174,425.05




5. Joe decides to buy land as a hedge against inflation. He finds 100 acres for sale at $3000

per acre. Land values in this area consistently appreciate at an annual rate of 4%. If Joe

buys the property for $3000 per acre, what is the future value per acre at the end of 15

years, assuming a 4% annual appreciation rate?

PV = $ 3,000 per acre ( Initial value)


n = 1 (annual)

t = 15 years

FV = $ ? Future Value per acre

FV = PV (1 + i

n)

nt

FV = 3,000 (1 + . 04

1)

(1)(15)

FV = 3,000(1.04)15

FV = 3,000 X 1.800943506 FV = $5,402.83

6. A young business owner is preparing his 5 year business plan and is trying to determine

the impact of a 3% annual inflation rate to his operating expenses over the next 5 year

period. If his first years operating expense is $ 200,000, what is the expected operating

expense projection at the end of 5 years, assuming all expense inputs remain the same?



n = 1 (annual)

t = 5 years

FV = $ ? Projected expense end of year 5

FV = PV (1 + i

n)

nt

FV = 200,000 (1 + . 03

1)

(1)(5)

FV = 200,000(1.03)5

FV = 200,000 X 1.15927402 FV = $231,854.81



Present Value of a Dollar

7. Jill would like to buy a 15 year bond today that has a face value of $30,000 at its

maturity. If the bond pays 4.5%, compounded monthly, what is expected present value of

the bond?

FV = $ 30,000

i = 4.5 %, or .045 rate

n = 12 (monthly)

t = 15 years

PV = $ ? Present Value of bond

PV = FV

(1 + in)

nt PV = 30,000

(1 + . 045

12 )(12)(15)

PV = 30,000

(1.00375)180 PV =

30,000

1.961555008

PV = $15,293.98

8. Calculate the present value (purchase price) of a property that is expected to be sold for

$400,000 in 5 years, assuming an annual appreciation rate of 4%.

Formula:

FV = $ 400,000

i = 4 %, or .04 rate

n = 1 (annual)

t = 5 years

PV = $ ? Present Value of Property

PV = 400,000

(1 + . 04

1 )(1)(5)

PV = 400,000

(1.04)5 PV =

400,000

1.216652902 PV = $328,770.84



Present Value of a Dollar Per Period

9. The company you worked for the past 25 years plans to downsize operations and will

offer qualified employees early retirement packages. They offer you a choice of a) 20

years of equal monthly annuity payments of $2500 per month that guarantees a 4%

minimum return on the annuity investments; or b) a lump sum cash settlement of

$375,000. In this problem, you will determine a) the present value of the annuity (PV)

payments and b) which option provides the largest present value (PV).

c) Solve for present value of the annuity:

PMT = $ 2500 (payment)


n = 12 (monthly)

t = 20 years

PV = $ ? Present Value of Annuity

PV = PMT [(1 +

in)

nt

− 1]

(1 + in)

nt

∗ (in)

PV = 2,500

[(1 + . 0412

)(12)(20)

− 1]

(1 + . 0412 )

(12)(20)

∗ (. 0412 )

PV = 2,500 [(1.00333333)240 − 1]

(1.00333333)240 ∗ (0.00333333) PV =

2,500 [1.222580315]

2.222580315 ∗ 0.00333333

PV =3056.450787

0.007408594 PV = $412,554.77

d) Calculate the difference between the cash settlement and present value of the annuity.

Which is higher?

PV of Annuity (from part a) = $ ? 412,555

Cash settlement = $ 375,000 - 375,000

Net Difference = $ $37,555



Sinking Funds Factor

10. A young couple wants to buy 100 acres at the end of their first 10 years of farming and

wants to save enough funds for a 35% cash down payment. If the 100 acres will cost

$5000 per acre in 10 years, how much will they need for their 35% down payment? In

addition, how much do they need to invest semi-annually in an investment account to

then have the down payment amount if the account pays 3.75% annual rate of interest,

compounded semi-annually?

Problems:

a. How much down payment will be needed in 10 years (Future Value)?

100 acres x 5,000 per acre = $500,000 x .35 = $175,000 down payment

b. What is the semi-annual deposit required to meet the 35% cash down payment

needed in 10 years?

FV = $ ? (Answer from a. for down payment)


n = 2 (semi - annual)

t = 10 years

Pmt = $ ? Semi-Annual deposit

PMT = FV ∗

in

(1 + in)

nt

− 1

PMT = 175,000 ∗

. 03752

(1 + . 0375

2 )(2)(10)

− 1

PMT = 175,000 ∗ 0.01875

(1.01875)20 − 1

PMT = 3,281.25

0.449948026 PMT = $7,292.51



11. A young couple wants to buy their parents’ trucking business at the conclusion of the

next 3 years to coincide with their parents’ retirement. The operation consists of 4 over

the road tractor trailer units, and the parents have agreed to sell them at the end of 3 years

for $25,000 each.

Problems:

a. How much is needed to complete the purchase at the end of 3 years?

4 x 25,000 = $100,000

b. How much will the couple need to invest into their savings account quarterly if

interest is compounded quarterly with a 4.75% nominal rate of interest to

complete this purchase?

FV = $ ? (From a. above Future Value)


n = 4 (quarterly)

t = 3 years

PMT = 100,000 ∗

. 04754

(1 + . 0475

4 )(4)(3)

− 1

PMT = 100,000 ∗ 0.011875

(1.011875)12 − 1

PMT =1187.50

0.15218546 PMT = $7,802.98


Economic Principles in Agribusiness: Time Value of Money Teacher Note

Note to Teachers for Problem Solving

The student needs to be proficient in the use of the scientific calculator for algebraic calculations.

It is recommended students review calculator functions and practice working with the formula

steps. A number of the formulas have similar calculations.

The students should be reminded to look at the results and determine if the answer they have

calculated is reasonable or not. Re-doing the calculations is strongly recommended. A variance

in answers to the “Answer Key” should be allowed due to rounding and truncating some of the

decimals. Students should be reminded to use rules learned in algebra.

Steps in Calculating Problems

1. Review calculators following functions:

a. Exponent ^ carrot key is used to raise to the power

b. ANS [ ANS ] provides answer for the calculation

c. Negative sign [ ( -- ) ] use to enter a negative number and then press =. In

the six functions formula, only amortization uses the negative sign.

d. Enter [ Enter ] Be sure to hit enter after each calculation!

e. Clear Button CLEAR Make sure to clear before all calculations.

2. Read the questions more than once. Go back; write down what is given in the problem.

3. Write the formula to be used to solve the problem; then substitute in the formula what is

known and what is to be solved for.

4. Calculate parenthesis first for both the numerator and denominators in the formula.

5. Next calculate the Exponent for numerator and denominators in the formula.

6. Limit rounding and /or truncating. It is best to let the calculator calculate and use the

calculated factor for the next step. If rounding, round to no less than five or six numbers

right of decimal point.

7. Next calculate the brackets, if in the problem

8. Follow progression of calculations left to right, reducing factors to decimal form for a

multiplying factor to arrive at desired answer.

9. Recommend practice of calculating the following calculations:

a. Parenthesis calculations: ( i ) = interest expressed as decimal. Example .06 and

(n) represents number of compound periods (example: 12 (monthly); 4

(quarterly); 2 (semi-annual) and 1 (annual)). In below example, ( i ) = .06 ( n)

= 12 ( 𝑖

𝑛) = (

.06

𝟏) = 0.06

b. Parenthesis calculation plus 1: Same example above, plus


Economic Principles in Agribusiness: Time Value of Money Teacher Note

(1 + 𝑖

𝑛) = (1 +

.06

1) = (1 + 0.06) = 1.06

c. Parenthesis calculation plus 1 with exponent ( ^ ) (carrot key) calculation added:

In this example, we use the( ^ )function to raise the sum calculated in parenthesis

to the exponent [exponent factor is the number of compound periods (n) times the

number value of time (t)]. In this example,

(n) =1 compound period; (i ) = .06 Interest ( t) = 5 years

Same example above, plus exponent of 5 represents time and 1 represents number

of compound periods (annual):

(1 + 𝑖

𝑛)

(𝑛)∗(𝑡)

= (1 + .06

1)

(1)∗(𝟓)

= (1 + 0.06)𝟓 = (1.06)𝟓 = 1.338225578

In the above formula, from left to right one would follow these steps:

Step one: Write the formula

Step two: Substitute the known factors. In above, substitute for ( i ) ,( n ) and

( t ).

Step three: Calculate the fraction first and enter as decimal. Then calculate

exponents to find the total number of compounding periods (exponent) and enter

as the exponent sum (5 above).

Step four: Add 1 + the decimal 0.06 then press Enter ( let calculate, next press

^ carrot key), then enter the exponent (above number = 5) which equals total

number of compounding periods (n) times number of years ( t ), then press Enter

key. This number is normally expressed with eight + numbers right of decimal

point. It is best not to round or truncate this number, but if rounded, carry out to a

minimum of 5 numbers right of decimal point. Note, if formula calls for a

negative exponent, as in the amortizations, enter your number first, press enter,

the ^, next press [ (--) ] to enter as negative exponent, enter your exponent and

let calculate for answer.

We recommend following these steps in calculations or steps students are

comfortable with as some may opt to use substitutions.

Teachers and advisors may opt to use a financial calculator for alternative checks.

Many businesses use the HP 12C financial calculators which easily calculate the

six functions.

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