Final answer:
The student's question entails calculating the annual deposit required for an endowment fund to produce a $3,000,000 annuity at a 9% interest rate, using the future value of an annuity formula.
Step-by-step explanation:
The student's question revolves around finding the annual deposit amount required to accumulate a specific endowment fund that will provide the World Wide Hunger Fund with $3,000,000 per year into perpetuity, given a 9 percent interest rate. This is a present value of annuity problem in finance, which uses the formula for the present value of an annuity to find out the amount that must be deposited annually.
The formula for the present value of an annuity is PVA = PMT × [(1 - (1 + r)^-n) / r], where PVA is the present value of an annuity, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.
To provide $3,000,000 into perpetuity at a 9% interest rate, the endowment fund itself needs to be $3,000,000 / 0.09, which equals $33,333,333.33. Using the present value of an annuity formula, we can solve for PMT (the annual deposit).
However, since the answer requires the annual deposit to simply accumulate to the present value instead of considering perpetuity, we would calculate it differently, using the formula of a future value annuity. We must find the annual deposit (PMT) that will grow to $33,333,333.33 after 5 years at a 9% interest rate.
The formula for the future value of annuity is FVA = PMT × [((1 + r)^n - 1) / r]. By rearranging the formula to solve for PMT, we get PMT = FVA / [((1 + r)^n - 1) / r]. Substituting the given values (FVA = $33,333,333.33, r = 0.09, n = 5) into the formula will yield the correct annual deposit.
Once the calculation is done appropriately, the correct choice can be selected from the given options.