Question

An investor needs ​$18000 in 10 years.

​(a) What amount should be deposited in a fund at the end of each quarter at 9​% compounded quarterly so that there will be enough money in the​ fund?
​(b) Find the​ investor's quarterly deposit if the money is deposited at ​4.5% compounded quarterly.

Answer 1

(a) Let P be the amount deposited at the end of each quarter. Then, the future value F after n quarters is given by

F = P(1 + 0.09)^n

Given that there must be enough money in the fund, we can set F = A, the amount required. Therefore,

A = P(1 + 0.09)^n

Solving for P,

P = A(1 + 0.09)^-n

(b) Let P be the amount deposited at the end of each quarter. Then, the future value F after n quarters is given by

F = P(1 + 0.045)^n

Given that there must be enough money in the fund, we can set F = A, the amount required. Therefore,

A = P(1 + 0.045)^n

Solving for P,

P = A(1 + 0.045)^-n