Petroleum Project Economics 03

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Petroleum Project

EconomicsEcon210D

Presentation 3

Interest and Time Value of Money

Week 31


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Interest remains constant each year. Interest is not reinvested

Interest is calculated by the formula.

2

Simle Interest

nrPI =

where: I = Interest, P = Principal, r =

interest, n = number of years.

Interest and Time alue of !oney"ee# $


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Interest is based on principal plus reinvested interest

from previous years

Interest increase each successive year

$

!omound Interest

( )nrPA += 1where: P = Principal, r = interest, n =

number of years, % = Principal & Interest,



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'

"uture and Present Value

(uture alue ) the value at some point inthe future of a sin#lecash flow or aseriesof cash flows in the future.

Present alue ) the value today of asin#lecash flow or a seriesof cash flowsin the future

alues chan*e over time due to interest

Interest is based on compound interestInterest and Time alue of !oney

"ee# $


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+

where:

F = Future value

I = Investment/Principalr = rate of interest (for each timeperiod)n = number of time periods.

"uture Value

[ ]

n

rIF

1



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Present Value

[ ]

n

r

IP1

where:

P = Present value

I = Investment/Principalr = rate of interest (for each timeperiod)n = number of time periods.



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-

"uture Value of a Sin#le !as$

"lo%

%n investor deposits 1// into an account

which offers 120 p.a. compound interest.

"hat is the value of the investment at the

end of $ years



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Present Value of a Sin#le !as$

"lo%

%n investor is supposed to receive 1// in

$ years time. If the rate of compound

interest is 120 p.a. what is the present

value of the amount



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3

&nnuities ' Series of !as$ flo%s

%n annuityis a seriesof e4ual paymentsat evenly spaced intervals

The payments occur at the (e#innin#ofeach period for an annuity duewhile theyoccur at the endof each period for anordinary annuity

Interest is earned on amounts paid



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1/

%nnuity 5ue and an 6rdinary %nnuity ) over

$ years

%nnuity 5ue

6rdinary %nnuity

Jan 1st2009

1// 1// 1//

1//1// 1//

Jan 1st2009

Jan 1st2010 Jan 1st2011 Dec 31st2011

Dec 31st2009 Dec 31st2010 Dec 31st2011



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11

%t the (e#innin#of each year an

investor deposits 1// into an account

which offers 120 p.a. compund

interest. "hat is the value of the

investment at the end of $ years

"uture Value of an &nnuity Due



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12


Time )ear &mount Workin#s "uture Value

*an 1st 200+ / 1// 1'/

*an 1st 2010 1 1// 12+

*an 1st 2011 2 1// 112

Dec 31st 2011 $ / /

Total $// $-



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1$




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1'

(uture alue of an %nnuity 5ueusin* (ormula

where

I = periodic investment

r = interest rate per period

n = number of periods

111

1

r

rIFVA

n

DUE



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1+

%t the endof each year an investor

deposits 1// into an account which

offers 120 p.a. compound interest.

"hat is the value of the investment at

the end of $ years

"uture Value of an ,rdinary

&nnuity



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1


&nnuity

Time )ear &mount Workin#s "uture Value

*an 1st 200+ / / /

Dec 31st200+ 1 1// 12+

Dec 31st2010 2 1// 112

Dec 31st 2011 $ 1// 1//

Total $// $$-



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1-


&nnuity



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1

(uture alue of an 6rdinary%nnuity usin* (ormula

where




r

rIFVA

n

ORDINARY

11



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13

%t the be*innin* of each year an

investor deposits 1/,/// into an

account which offers 1/0 p.a.

compound interest. "hat is the value of

the investment at the end of ' years

-uestion 1



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2/

%t the end of each year an investor

deposits 2,/// into an account

which offers 20 p.a. compound


investment at the end of + years

-uestion 2



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21

%t the end of each 4uarter an investor

deposits '// into an account which


"hat is the value of the investment at

the end of 1 year

-uestion 3



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22

%t the be*innin* of each month an




investment at the end of months

-uestion .



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2$

%t the (e#innin#of each year an


which offers 120 p.a. compund

interest. "hat is the present value of

the investment

Present Value of an &nnuity Due



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2'


Time )ear &mount Workin#s Present Value

*an 1st 200+ / 1// 1//

*an 1st 2010 1 1// 3

*an 1st 2011 2 1// /

Dec 31st 2011 $ / /

Total $// 23



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2+




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2

Present alue of an %nnuity 5ue7sin* the formula

=

11

11

1

r

rIPVA

n

DUE

where

I = periodic investment r = interest rate per period




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2-

%t the endof each year for $ years an



interest. "hat is the present value of the

investment

Present Value of an ,rdinary

&nnuity



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2


&nnuity

Time )ear &mount Workin#s Present Value

*an 1st 200+ / / /

Dec 31st200+ 1 1// 3

Dec 31st2010 2 1// /

Dec 31st 2011 $ 1// -1

Total $// 2'/



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23


&nnuity



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$/

Present alue of an 6rdinary%nnuity 7sin* the (ormula

=

r

rIPVA

n

ORDINARY

1

11

where



n = number of periodsInterest and Time alue of !oney"ee# $


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$1

%t the be*innin* of each year an

investor deposits 1/,/// into an

account which offers 1/0 p.a.

compound interest. "hat is the present

value of the investment if this is done

over ' years

-uestion /



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$2

%t the end of each year for + years an

investor deposits 2,/// into an

account which offers 20 p.a.

compound interest. "hat is the

present value of the investment

-uestion



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$$

%t the end of each 4uarter an investor

deposits '// into an account which


"hat is the present value of the

investment if this is done over 1

year

-uestion



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$'

%t the be*innin* of each month for

months an investor deposits 1// into

an account which offers 120 p.a.

compound interest. "hat is the

present value of the investment

-uestion

Interest and Time alue of !oney" # $

Petroleum Project Economics 03

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