Compound Interest

Compound Interest

The interest is added to the principal and that amount becomes the principal for the next calculation of interest.

OR

Interest Period (compounding Period): The amount of time which interest is calculated and added to the principal. It could be a year, a month, a week and so on.

Find the period interest rate for:

• A 12% annual interest rate with 4 interest periods per year.

•3%

• An 18% annual rate with 12 interest periods per year.

•1% ½

• An 8% annual rate with 4 interest periods per year.

•2%

Find the Future Value

Using the simple interest formula method:

1. Find the end of period principal: multiply the original principal by the sum of 1 and the period interest rate.

2. For each remaining period in turn, find the next end of period principal: multiply by the previous end of period principal by the sum of 1 and the period interest rate.

3. Identify the last end-of-period principal as the future value.

Look at this example

Find the future value of a loan of $800 at 13% for three years.

• The period interest rate is 13% since it is calculated annually.

• First end-of-year = $800 x 1.13 = $904

• Second end-of-year =$904 x 1.13 = $1021.52

• Third end-of-year = $1021.52 x 1.13 = $1,154.32

• The FV of this loan is $1,154.32

Find the compound interest

• Compound interest =

future value – original principal.

• In the previous example, the compound interest is equal to the future value – original principal.

• CI = $1,154.32 - $800 = $354.32

• The compound interest = $354.32

Derivation of the Formula

Amount at beginning of the interest period

+ interest for period

= Amount at end of interest period

First yearP+ iP=P(1+i)

Second yearP(1+i)+ iP(1+i)=P(1+i)2

Third yearP(1+i)2+ iP(1+i)2=P(1+i)3

Nth yearP(1+i)n-1+ iP(1+i)n-1=P(1+i)n

Examples

• If 500$ were deposited in a bank savings account, how much would be in the account three years hence if the bank paid 6% interest compounded annually?

Examples

• If you wished to have 800$in a savings account at the end of four years, and 5% interest was paid annually, how much should you put into the savings account now?