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.
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.