Question

A family wishes to accumulate $400,000 in a college fund at the

end of 15 years. How much should the initial investment be if the
fund earns 8% compounded quarterly?

Answer 1

$177,107.70

Explanation:

We Know

- A family wishes to accumulate $400,000 in a college fund at the

end of 15 years.

- 8% compounded quarterly

How much should the investment be?

We use the formula:

FV = PV(1 + r/n)^(n·t)

PV = present value (or initial investment)

r = annual interest rate

n = number of compounding periods per year

t = number of years

FV = $400,000

r = 8% = 0.08

n = 4 (quarterly compounding)

t = 15 years

$400,000 = PV(1 + 0.08/4)^(4·15)

$400,000 = PV(1.02)^60

PV = $400,000 / (1.02)^60

PV ≈ $177,107.70

So, the investment should be $177,107.70