In 30 years, you plan to set up a fellowship fund for your university that pays out $100,000 each year in perpetuity with an annually compounded discount rate of 5%.In order to set up the fund in 30 years, how much do you need to save each year (starting at the end of this year)assuming you can get a semi-annually compounded return of 10% on your savings for the next 30 years?
A)$66,666.67
B)$11,595.56
C)$21,215.49
D)$30,744.90
E)$30,000.00

Question

Quizplus · Accepted Answer

First, we need to calculate the amount we need to save each year to accumulate enough capital in 30 years to pay out $100,000 annually in perpetuity.

Using the perpetuity formula, we can find that the present value (PV) of the perpetuity is:

PV = Payment / Discount rate
PV = $100,000 / 5%
PV = $2,000,000

Next, we need to calculate how much we need to save annually over the next 30 years to accumulate $2,000,000 at a semi-annual compounded rate of 10%.

Using the present value formula, we can find that the annual savings amount (PMT) is:

PMT = PV * (r / (1 - (1 + r)^(-n)))
PMT = $2,000,000 * (0.10 / (1 - (1 + 0.10)^(-60)))
PMT = $11,595.56

Therefore, we need to save $11,595.56 annually, starting at the end of this year, in order to accumulate $2,000,000 in 30 years and set up the fellowship fund that pays out $100,000 annually in perpetuity.

The correct answer is B.

In 30 Years, You Plan to Set Up a Fellowship