Questions: You want to endow a scholarship that will pay 8,000 per year forever, starting one year from now. If the school's endowment discount rate is 8%, what amount must you donate to endow the scholarship? The amount you must donate to endow the scholarship is . (Round to the nearest cent.)

You want to endow a scholarship that will pay 8,000 per year forever, starting one year from now. If the school's endowment discount rate is 8%, what amount must you donate to endow the scholarship?

The amount you must donate to endow the scholarship is . (Round to the nearest cent.)

Transcript text: You want to endow a scholarship that will pay $\$ 8,000$ per year forever, starting one year from now. If the school's endowment discount rate is $8 \%$, what amount must you donate to endow the scholarship? The amount you must donate to endow the scholarship is $\$$ $\square$ . (Round to the nearest cent.)

Solution

Solution Steps

To determine the amount needed to endow a scholarship that pays a fixed amount annually forever, we use the concept of a perpetuity. The formula for the present value of a perpetuity is given by the annual payment divided by the discount rate. In this case, the annual payment is $8,000 and the discount rate is 8%.

Step 1: Identify the Type of Financial Instrument

The problem involves a perpetuity, which is a type of financial instrument that pays a fixed amount indefinitely. The formula for the present value of a perpetuity is:

\[ PV = \frac{C}{r} \]

where $ C $ is the annual payment and $ r $ is the discount rate.

Step 2: Substitute Given Values into the Formula

Given that the annual payment $ C = 8000 $ and the discount rate $ r = 0.08 $, we substitute these values into the formula:

\[ PV = \frac{8000}{0.08} \]

Step 3: Calculate the Present Value

Perform the division to find the present value:

\[ PV = 100000 \]