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 researchforever.The scientistShe 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 find the amount required to accumulate, we can use the perpetuity formula:
PV = PMT / r
where PV is the present value, PMT is the annual payment, and r is the annual interest rate.
Plugging in the values, we get:
PV = 1,000,000 / 0.06 = 16,666,667
This is the amount the inventor needs to have in her account on her fiftieth birthday. To find the annual deposit required, we can use the present value formula:
PV = PMT * [1 - (1 + r)^(-n)] / r
where n is the number of years until the endowment is funded.
Plugging in the values, we get:
16,666,667 = PMT * [1 - (1 + 0.06)^(-10)] / 0.06
Solving for PMT, we get:
PMT = 1,264,446
Therefore, the inventor must deposit $1,264,446 each year to accumulate the required amount of $16,666,667 in 10 years at a 6% interest rate. Choice C is correct.

A Wealthy Inventor Has Decided to Endow Her Favorite Art