Rocky Corp. anticipates needing a new vehicle for its President 4 years from now. It believes the vehicle will cost $32,000 in four years. How much will the company need to save on a bi-annual (i. e., twice per year) basis starting six months from now if it believes it can earn 10 percent on the amount it saves

The company need to save $3,351 on a bi-annual basis.

Explanation:

A fix Payment for a specified period of time is called annuity. The compounding of these payment on a specified rate is known as future value of annuity. In this question the company has to make a future value of $32,000 after 4 years at 10% interest rate.

We can calculate the amount of saving per year by calculating using following formula

Future value of annuity = FV = P x ([ 1 + r ]^n - 1) / r

Where

Future value = FV = $32,000

r = rate of return = 10% / 2 = 5% = 0.05

n = number of payments = 4 years x 2 payments per year = 8 payments

Placing Value in the formula

$32,000 = P x ([ 1 + 0.05 ]^8 - 1) / 0.05

$32,000 = P X 9.5491

P = $32,000 / 9.5491

P = 3,351.1