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If you want to save \$25,000 for a down payment on a house and you have ten years to save this amount, how much would you need to save monthly to achieve this goal if the interest rate is 5% compounded monthly? What happens if you can increase your interest rate to 8%? Come up with your own example of compound interest different than the one in question.

## SOLUTION This solution is FREE courtesy of BrainMass!

In this problem, we are calculating the future value of an annuity.

Let C represent the amount of money saved every month, then:
FV=C/i*((1+i)^n-1)
FV = \$25000
Time = 10 years
Number of compounding periods n= 12*10=120 (compounding is done monthly)
Interest rate = 5% per annum
Interest rate for the compounding period (monthly) i= 5%/12

Then we have:
25000 = C/(5%/12)*((1+(5%/12))^120-1)
25000=C*155.28
C=\$161 per month

When interest rate is 8% per annum:
25000 = C/(8%/12)*((1+(8%/12))^120-1)
25000=C*182.95
C=\$136.65 per month

My chosen interest rate 12%:
25000 = C/(12%/12)*((1+(12%/12))^120-1)
25000=C*230.04
C=\$108.68 per month

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