Question

The parents of a one-year-old boy plan to invest for his college education. Their target is that when he is 18 years old, the fund should have the amount of $75,000.

(a) If the interest is at the annual rate of 4.6%, compounded monthly, then the initial amount needed to set up the fund now is ___________$ X .
(b) If the interest is at the annual rate of 6.7%, compounded monthly, then the initial amount needed to set up the fund now is___________ $
(c) If the interest is at the annual rate of 9.3%, compounded continuously, then the initial amount needed to set up the fund now is___________ $ X .

Answer 1

a. $34,363.09

b. $24,086.61

$15,432.69

Explanation:

The formula for calculating present value =

P = FV (1 + r/m)^-mn

FV = Future value

P = Present value

R = interest rate

N = number of years

m = number of compounding

a. $75,000 ( 1 + 0.046 / 12) ^-12x17 = $34,363.09

b. $75,000 ( 1 + 0.067 / 12) ^-12x17 = $24,086.61

present value with continuous compounding

PV = FV / е^rn

c. $75,000 / е^0.093 x17 = $15,432.69