Parents have setup an account in order to have 12000 in 10 y

Parents have setup an account in order to have $12,000 in 10 years for their child’s college fund. How much should be deposited quarterly into the account paying 4.5% compounded semiannually?

Solution

lets say $ P is deposited quarterly

applying compounded quarterly formula

A = P ( 1+ r/n)^nt

12,000 = P ( 1+ .045 /4 )^40

solving for P

P = $ 7670.79

therefore, $ 7670.79 must be deposited quarterly

12000 = P ( 1+ .045/2)^20

P = 7689.8

and $ 7689.8 must be deposited semiannually