You have a goal to raise $1000 in four years' time.If your mother gives you $400 at the end of the first year,you make six deposits of equal amounts every six months thereafter,and all the money is deposited in a bank,which pays 8% p.a. ,compounded semi-annually,how large must each of the six payments be for you to reach your target?
A)$74.46
B)$65.55
C)$82.74
D)$77.26

Question

Quizplus · Accepted Answer

The future value of the $400 at the end of the first year is $400(1.04)^2 = $432.16. The future value of the six equal payments at the end of the fourth year is 6P(1.04)^8, where P is the amount of each payment. The total future value of all the deposits is $432.16 + 6P(1.04)^8. This must be equal to $1000, so we have the equation $432.16 + 6P(1.04)^8 = $1000. Solving for P, we get P = $74.46.

You Have a Goal to Raise $1000 in Four Years