Question

You have been paying $1000 every month for 6 years to a friend of yours who is extremely lazy to find a job. The annual interest rate is 9%. What is the worth of your money after 6 years with:
a) Annual compounding
b) Every-six-months compounding

Answer 1

Compounding interest on any principal amount can be calculated by the following formula:
A = P [ 1 + (r/n)] ^nt
A = Total amount after compounding
P = Principal amount
r = Rate of interest
n = Number of times compounding is done
t = total time period

i) Annual compounding:
A = Total amount after compounding
P = Principal amount = $1000
r = Rate of interest = 9% = 0.09
n = Number of times compounding is done = 1 (annual compounding)
t = total time period = 6 years

Hence from A = P [ 1 + (r/n)] ^nt
A = 1000 * [ 1+(0.09/1) ^1*6
= 1000 * [ 1 + 0.09 ] ⁶
= 1000 * 1.09⁶
= 1000 * 1.677
= 1677.100

Hence due to annual compounding, the final worth of $1000 would be $1677.10

ii) Six - months compounding
A = Total amount after compounding
P = Principal amount = $1000
r = Rate of interest = 9% = 0.09
n = Number of times compounding is done = 6 (six - month compounding)
t = total time period = 6 years

Hence from A = P [ 1 + (r/n)] ^nt
= 1000 * [ 1 + (0.09/6)] ^6*6
= 1000 * [ 1 + 0.015 ] ³⁶
= 1000 * 1.015³⁶
= 1000 * 1.709
= 1709.14

Hence due to six months compounding, the final worth of $1000 would be $1709.14