Question

Your dad's older sister just turned 65 and is going to retire. She is thinking about the future and wants to have a steady stream of money to live on for retirement, plus provide income for her heirs after she is gone. She has enough money to buy a perpetuity that will pay her $75,000 one year after she purchases it and then pays her an additional 3.5% every year after that (to keep up with inflation).

a. Assuming that the perpetuity is held in an investment that will grow at 8% annually, what price will your aunt pay for the perpetuity?
b. If she purchases the perpetuity, she will receive a payment of $75,000 in one year. What will the payment be twenty years from the date of purchase?

Answer 1

To find the price for the perpetuity, use the formula PV = Payment / Interest Rate. To find the payment twenty years from the date of purchase, use the formula FV = PV * (1 + Interest Rate)^n.

Step-by-step explanation:

To find the price your aunt will pay for the perpetuity, we can use the formula for the present value of a perpetuity:

PV = Payment / Interest Rate

In this case, the payment is $75,000 and the interest rate is 3.5%. Plugging in these values, we get:

PV = $75,000 / 0.035 = $2,142,857.1429

So, your aunt will need to pay approximately $2,142,857.14 for the perpetuity.

To find the payment twenty years from the date of purchase, we can use the formula for the future value of a lump sum:

FV = PV * (1 + Interest Rate)^n

In this case, the PV is $75,000, the interest rate is 3.5%, and n is 20. Plugging in these values, we get:

FV = $75,000 * (1 + 0.035)^20 = $169,034.68

So, the payment twenty years from the date of purchase will be approximately $169,034.68.