Question

Annuities and Interest Rates. Professor´s Annuity Corp. offers a lifetime annuityto retiring professors. For a payment of $80,000 at the age 65, the firm will paythe retiring professor $600 a month until death. a. If the professor´s remaining life expectancy is 20 years, what is the monthly rateon this annuity? What is the effective annual rate?

Answer 1

To calculate the monthly rate on this annuity, we can divide the initial payment of $80,000 by the remaining life expectancy of 20 years, and then divide by 12 months:

Monthly rate = $80,000 / (20 years * 12 months) = $333.33

To calculate the effective annual rate, we can use the formula:

Effective Annual Rate = (1 + Monthly rate)^12 - 1

Plugging in the monthly rate we calculated:

Effective Annual Rate = (1 + 0.02778)^12 - 1 = 0.3586 or 35.86%

So, the monthly rate on this annuity is $333.33 and the effective annual rate is 35.86%.