Sampson, Inc. invested $1.325 million in a project that earned an 8.25% rate of return. Sampson sold their investment for $3,713,459. How much sooner could Sampson have sold the company if
They only wanted $3 million from the project?

Question

Quizplus · Accepted Answer

First, we need to find out how long it took for the project to earn $3,713,459:

PV + I = FV

where PV is the initial investment, I is the interest earned, and FV is the final value.

$1.325m + I = $3,713,459

I = $2,388,459

Now we can use the formula for the future value of an annuity to find out how long it would take for the project to reach $3 million:

FV = CF x [(1 + r)^n - 1] / r

where CF is the cash flow, r is the interest rate, and n is the number of periods.

$3m = CF x [(1 + 0.0825)^n - 1] / 0.0825

$2,388,459 = CF x [(1 + 0.0825)^n - 1]

CF = $226,496.60

$3m / $226,496.60 = 13.25

So it would take 13.25 periods to reach $3 million. Since the project earned an 8.25% rate of return, each period is equal to one year.

13.25 - 4 = 9.25

Therefore, Sampson could have sold the company 9.25 years sooner if they only wanted $3 million from the project. Rounded to the nearest year, the answer is 9. Answer choice A is the closest.