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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?