In 30 years,you plan to set up a fellowship fund for your university that pays out $100,000/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 this year)assuming you can get a semi-annually compounded return of 10% on your savings for the next 30 years?

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the perpetuity that will be created in 30 years. Using the perpetuity formula, we get:

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

Next, we need to calculate the amount we need to save each year to reach $2,000,000 in 30 years. We can use the annuity formula for this:

PV = Payment x (1 - (1 + r/n)^(-nt)) / (r/n)
$2,000,000 = Payment x (1 - (1 + 10%/2)^(-2*30)) / (10%/2)
$2,000,000 = Payment x 34.67584008

Payment = $57,750.72

Therefore, we need to save $57,750.72 each year for the next 30 years to reach our target of $2,000,000.

In 30 Years,you Plan to Set Up a Fellowship Fund