Professor%u2019s Annuity Corp. offers a lifetime annuity to retiring professors.
ID: 2699127 • Letter: P
Question
Professor%u2019s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $88,000 at age 65, the firm will pay the retiring professor $800 a month until death.
If the professor%u2019s remaining life expectancy is 20 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.)
If the monthly interest rate is 1%, what monthly annuity payment can the firm offer to the retiring professor? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
a.If the professor%u2019s remaining life expectancy is 20 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.)
Explanation / Answer
a. PV = 88000, PMT = 800 pm
nper = 20Yr*12month/Yr = 240 period
So Monthly Rate = Rate(nper,pmt,PV,FV)
= Rate(240,800,88000,0)
= 0.76%
annual rate = 12*0.76% = 9.12%
EAR = (1+i/n)^n -1 = (1+9.12%/12)^12-1 =9.51%
b. Montly Rate = 1% PV = 88000, PMT = ?
nper = 20Yr*12month/Yr = 240 period
So Monthly Annuity = PMT(Rate,nper,PV,FV)
= PMT(1%,240,-88000,0)
= $968.96
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