The Study of Money Simple Interest For most of your financial plans, throughout your life, there will be two groups involved. The Bank The Individual.

The Study of Money

Simple Interest

For most of your financial plans, throughout your life, there will be

two groups involved.

The Bank The Individual

There will be times when you find yourself in a situation where you

need more money than you have…

• To purchase a house

• To purchase a car

• To get married

• To purchase furniture, a stereo, a special trip…..

Where does the money come from?

Typically, people will go to a bank for a loan.

Banks will loan you money….but not for free….

Interest is the fee charged for the use of money.

•Interest can be calculated two different ways:

• simple or compound.

For simple interest,

the bank charges you a certain percentage of the loan amount.

• Simple Interest is calculated using:

I = Prt

I = Interest (cost of the loan)

P = Principle (amount of the loan)

r = rate (interest rate, as a decimal)

t = time (number of payment cycles)

You go on a trip to the Caribbean with your friends for March Break.

It is all inclusive, at a cost of $1800.00, and you pay with your new credit card.

Your CC charges 18% interest per year, which works out to be 1.5% per month.

(18% / 12 months = 1.5%)

What is the monthly interest charge?

I = Prt P = 1800, r = 0.015, t = 1

I = 1800(0.015)(1)= $27

So, you would owe the bank $1800.00, plus $27.00 interest.

Suppose you paid $200.00 off the debt. That means for the next month, they would use $1600.00 for the calculation ($24.00) interest.

You would pay interest to the CC company until you paid the entire debt.

• As with any equation, as long as you are given three of the variables, you can solve for the fourth….

Complete the given worksheets on simple interest before we move in to compound interest.

• While simple interest offers a good initial illustration, most of your dealings with the bank will involve another kind of interest calculation

• Compound Interest

Compound Interest

Since our first example involved you going into debt, let’s look at an example

where you will be earning money.

Examine the situation below:

Suppose you deposited $1000.00 into an account.

You can get 6% interest for 4 years.

How much will you end up with in your account?

Our calculations are very similar to the simple interest formula.

We take our starting amount ($1000.00),

and multiply by our interest rate (6% in decimals = 0.06)

Note: Because after each year you want to know how much in total is in your

account, not just the interest, we add a “1” to the calculation.

So for 6% interest, we multiply by “1” plus 0.6, which equals1.06

1000(1.06) = 1060.00

Start with Interest Amount in the bank after the first year

1060(1.06) = 1123.60

Now Start with

Interest Amount in the bank after the second year

1123.60(1.06) = 1191.02

Now Start with

Interest Amount in the bank after the third year

• As a short cut:, we can do all the multiplications in one step

1191.02(1.06) = 1262.48

Now Start with

Interest Amount in the bank after the fourth year

1000(1.06)(1.06)(1.06)(1.06) = 1262.48

These can be compressed into a power! so…

1000(1.06)4 = 1262.48

Could we just jump to the final stage given just the

initial values? YES!

Suppose you deposited $1000.00 into a savings account. If you could

get 6% for 4 years, how much would you end up with?

1000(1.06)4 = $1262.48P (1 + i) n = A

Replace the numbers with variables

Amount formula for compound interest

A = P(1 + i)n

A = Final AmountP = Starting Principlei = interest (always in decimals)n = number of cycles (months,

years…

Invest $1000.00 at 4.25% for 7 years.

How much will you have?

A = P(1 + i)n

P = 1000.00, i = 0.0425, n = 7

A = 1000(1 + 0.0425)7

= 1000(1.0425)7

= $1338.24

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