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 for research.The scientist 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

To accumulate to $1,000,000 per year for research, the total accumulated amount in the endowment after 10 years must be:

$1,000,000 / 0.06 = $16,666,667

To find out how much the inventor needs to deposit each year, we can use the present value of an annuity formula:

PMT = PV * r / ((1+r)^n - 1)

where PMT is the annual payment, PV is the present value we want to accumulate, r is the interest rate per period, and n is the number of periods.

In this case, PV is $16,666,667, r is 6% or 0.06, and n is 10. Plugging in these values, we get:

PMT = $16,666,667 * 0.06 / ((1+0.06)^10 - 1) = $1,264,446

Therefore, the inventor must deposit $1,264,446 each year to accumulate $16,666,667 in 10 years and provide $1,000,000 per year for research. The answer is C.

A Wealthy Inventor Has Decided to Endow Her Favorite Art