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Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $71,000 at age 65, the firm will pay the retiring professor $375 a month until death. a. If the professor’s remaining life expectancy is 20 years, what is the monthly interest rate on this annuity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

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TomShelby

Answer:

with a life expectancy of 20 years the annuity will yield: 0.21% per month

Explanation:

We will calcualte the monthly interest rate of an annuity of 375 for 20 years which PV is 71,000

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 375

time 240 (20 years x 12 months a year)

PV $71,000.00

[tex]375 \times \frac{1-(1+r)^{-240} }{r} = 71,000\\[/tex]

We can solve for rate using excel goal seek:

we write any number value on cell A1

then on any other cell we write:

=PV(A1,240,375)

then we will use goal seek and define:

this cell, with the value of 71,000 changing A1

rate = 0.002053645 = 0.21% per month

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