A wealthy inventor has decided to endow her favorite art museum by establishing funds for an endowment which would provide $1,000,000 per year forever. She will fund the endowment upon her fiftieth birthday 10 years from today. She plans to accumulate the endowment by making annual end-of-year deposits into an account. The rate of interest is expected to be 6 percent in all future periods. How much must the scientist deposit each year to accumulate to the required amount?
A) $1,575,333
B) $736,000
C) $1,264,446
D) $943,396

Question

Quizplus · Accepted Answer

The present value of perpetuity (PV) formula is PV = PMT/i, where PV is the present value, PMT is the payment amount, and i is the interest rate.
In this case, the desired perpetuity payment is $1,000,000 per year, and the interest rate is 6%. Therefore, the present value of the perpetuity is:
PV = $1,000,000/0.06 = $16,666,667
This is the amount the scientist needs to accumulate by the end of year 10.
We can use the future value of an annuity (FVA) formula to find out how much to deposit each year. The FVA formula is:
FVA = PMT x [(1 + i)^n - 1]/i, where FVA is the future value, n is the number of periods, and all other variables are the same as before.
We need to solve for PMT in this case. Plugging in the values we know, we get:
$16,666,667 = PMT x [(1 + 0.06)^10 - 1]/0.06
Solving for PMT, we get:
PMT = $1,264,446
Therefore, the scientist needs to deposit $1,264,446 at the end of each year, starting 10 years from today, in order to accumulate enough to provide a perpetuity payment of $1,000,000 per year forever. The answer is choice C.

A Wealthy Inventor Has Decided to Endow Her Favorite Art