Joe has $100,000 in an investment account. He is looking to retire in 12 years. He needs a minimum of $240,000 in order to retire. What rate of return does Joe need to make on his investment in order to be able to retire?

Present value (PV) = $100,000

Number of years (n) = 12 years

Future value (FV) = $240,000

FV = PV (1 + r) n

$240,000 = $100,000 (1 + r) 12

$240,000 = (1 + r) 12

$100,000

2.4 = (1 + r) 12

12√2.4 = 1 + r

1.0757 - 1 = r

0.0757 = r

r = 0.0757 = 7.57% = 8%

Explanation:

In this case, we need to apply the formula for future value of a lump sum (single investment). The present value, future value and number of years have been provided in the question with the exception of interest rate. Thus, interest rate becomes the subject of the formula, which implies that we will solve for interest rate.