When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers o

Question

When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $8. Based on actuarial tables, “Joltin’ Joe” could expect to live for 25 years after the actress died. Assume that the EAR is 8.9 percent. Also, assume that the price of the flowers will increase at 3.8 percent per year, when expressed as an EAR. Assume that each year has exactly 52 weeks, and Joe began purchasing flowers the week after Marilyn died. What is the present value of this commitment?

Explanation / Answer

Solution: To find the Present Value, we need to find Effective Annual Rates for a week Real EAR= (1+R)=(1+r)(1+h) 1+0.089 =(1+r)(1+0.038) 1.089=(1+r)(1.038) 1.089=1.038+1.038r 1.089-1.038=1.038r 0.051 1.03r r= 0.051/1.03 r= 4.9514563 Real EAR = 4.95% To find Weekly interest rate, we need to find the APR EAR= 4.95% m 52 weeks EAR=(1+(APR/m)^m-1 APR= m((1+EAR))^1/52-1) 52*((1+0.0495)^0.019230769-1) 52*((1.0495)^0.019230769-1) 0.048336311 APR = 4.83% Weekly Interest Rate = (APR/52) 0.0483/52                                                   0.00093 0.092884615 APR= 0.093% Present Value of the Cost of Roses is = PVA C((1-(1/(1+r)^t))/r) 7((1-(1/1+0.00093)^30*52))/0.00093) 7*({1-[1/1.00093)^1560]}/0.00093) 7(823.64238) 5765.4967 $5765.50

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