Question

Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $87,000 at age 65, the firm will pay the retiring professor $775 a month until death.

a. If the professor’s remaining life expectancy is 15 years, what is the monthly interest rate on this annuity? What is the effective annual Rate Monthly rate on annuity = _________ %
b. What is the effective annual interest rate? (Use the monthly rate computed in part (a) rounded to 2 decimal places when expressed as a percent. Enter your answer as a percent rounded to 2 decimal places.)Effective annual rate = ___________%
c. If the monthly interest rate is .75%, what monthly annuity payment can the firm offer to the retiring professor? Monthly annuity payment = $ ___________

Answer 1

To find the monthly interest rate, use the present value formula. The effective annual interest rate can be found using the monthly rate. To find the monthly annuity payment, use the present value formula.

Step-by-step explanation:

To find the monthly interest rate on the annuity, we need to calculate the present value of the annuity. The present value (PV) can be calculated using the formula:

PV = Payment / (1 + r)^n

Where Payment is the monthly payment, r is the monthly interest rate, and n is the number of months. Rearranging the formula to solve for r:

r = (Payment / PV)^(1/n) - 1

Plugging in the values, we get:

r = (775 / 87000)^(1/180) - 1 = 0.312% (rounded to 3 decimal places)

The effective annual interest rate can be found using the formula:

Effective annual rate = (1 + r)^12 - 1

Plugging in the monthly interest rate, we get:

Effective annual rate = (1 + 0.312%)^12 - 1 = 3.892% (rounded to 3 decimal places)

If the monthly interest rate is 0.75%, we can find the monthly annuity payment using the formula:

Payment = PV * r / (1 - (1 + r)^(-n))

Plugging in the values, we get:

Payment = 87000 * 0.75% / (1 - (1 + 0.75%)^(-180)) = $998.86 (rounded to 2 decimal places)