Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $74,000 at age 65, the firm will pay the retiring professor $450 a month until death.

Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $74,000 at age 65, the firm will pay the retiring professor $450 a month until death.

a.	If the professor’s remaining life expectancy is 15 years, what is the monthly rate on this annuity? What is the effective annual rate? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Monthly rate on annuity	%
Effective annual rate	%

b.	If the monthly interest rate is .75%, what monthly annuity payment can the firm offer to the retiring professor? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Monthly annuity payment

$

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations.

a. 

This is an annuity problem; use trial-and-error to solve for r in the following equation:

Using a financial calculator, enter PV = (−)74,000, n = 15 × 12 = 180 months

FV = 0, PMT = 450, compute i. To compute EAR:

EAR = (1 + 0.001)12 − 1 = 0.0121 = 1.21%

b.

Compute the payment by solving for C in the following equation:

Using a financial calculator, enter n = 180, i = 0.75%, FV = 0, PV = (−)74,000 and compute PMT = $750.56.