A wealthy art collector has decided to endow her favorite art museum by establishing funds for an endowment which would provide the museum with $1,000,000 per year for acquisitions into perpetuity. The art collector will give 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 art collector deposit each year to accumulate to the required amount?

Question

Quizplus · Accepted Answer

To find out how much the art collector must deposit each year to accumulate to the required amount, we can use the formula for the future value of an annuity:

FV = PMT × ((1 + r)n - 1) / r

where FV is the future value of the annuity, PMT is the annual deposit, r is the interest rate, and n is the number of years.

In this case, we want the future value to be $1,000,000 per year, the interest rate is 6%, and the number of years is 10 (since the art collector will start making deposits in 10 years and wants to accumulate the required amount by then).

So we have:

$1,000,000 = PMT × ((1 + 0.06)^10 - 1) / 0.06

Solving for PMT, we get:

PMT = $1,000,000 × 0.06 / ((1 + 0.06)^10 - 1) = $1264445.93

Rounding to the nearest dollar, the answer is (C) $1,264,446.

A Wealthy Art Collector Has Decided to Endow Her Favorite