Susan would like to have at least \$30,000 saved to help her son make a down payment on a home. If she invests \$20,000 in a savings account that pays 4% interest compounded quarterly, will she reach...

Susan would like to have at least \$30,000 saved to help her son make a down payment on a home. If she invests \$20,000 in a savings account that pays 4% interest compounded quarterly, will she reach her goal in 10 years? Justify your answer.

Asked on by lro1979

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to use the formula of compound interest such that:

`A = P(1 + i)^n`

A represents the final amount

P represents the invested amount

i represents the interest rate per period

n represents the number of compounding periods

The problem provides the value of P = \$20, 000 and the fact that the 4% interest is compounded quaterly, meaning that you may evaluate n such that:

`n = 10*4 = 40`  periods

`i = (4%)/4 => i = 0.04/4 => i = 0.01`

You may evaluate A such that:

`A = 20,000(1 + 0.01)^40 ~~ 29,777`

Hence, if Susan invests \$20,000 in a savings account that pays 4% interest compounded quarterly, the final amount, after ten years will be A = \$29,777, which is very close to the sum she needs, but a bit under \$ 30,000.

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