Question

Durban Moving and Storage wants to have enough money available 5 years from now to purchase a new tractor-trailer. If the estimated cost will be $240,000, how much should the company set aside each year if the funds earn 6% per year?

The company should set aside $  each year.

Answer 1

Here, we need to apply the formula for the future value of the annuity.

Future value of an annuity = P * ((1+r)ⁿ - 1)/r

Where, P = the annual payment, which is unknown

r = rate of interest = 6% = 0.06

n = number of years = 5

The required future value = $240,000

Putting the values in the formula, we get:

240,000 = P * ((1+r)ⁿ - 1)/r = P * ((1+0.06)⁵ - 1)/0.06

or, 240,000 = P* ((1.06)ⁿ - 1)/0.06

or, 240,000 = P* (1.34 - 1)/0.06

or, 240,000 = P* (0.34/0.06)

or, 240,000 = P* 5.67

or, P = 240,000/5.67 = $42,352.9

The company should set aside $42,352.9 each year.