Paul wants to invest a sum of money today that will accumulate to $50,000 at the end of 4 years. Assuming he can earn an interest rate of 8% compounded semiannually, how much must he invest today? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

He must invest $36,751

Explanation:

Future value is the sum of value of principal invested and compounded return received over the investment period.

Using following formula of future value to calculate the required interest rate.

FV  = PV x ( 1 + r )^n

FV = Future value = $50,000

n = number of years = 4 years

r = Interest rate = 8%

PV  = Present value = ?

$50,000 = PV x ( 1 + 8% )^4

$50,000 = PV x ( 1 + 0.08 )^4

$50,000 = PV x ( 1.08 )^4

$50,000 = PV x 1.3605

PV = $50,000 / 1.3605

PV  = $36,751.19