When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every
Sunday as long as he lived. A bunch of fresh flowers that the former baseball player thought appropriate
for the star cost about $5 when she died in 1962. Based on actuarial tables, “Joltin’ Joe” could expect to
live for 30 years after the actress died. Assume that the stated annual interest rate, compounded weekly, is
10.4 percent. Assuming that each year has exactly 52 weeks, what is the present value of this
commitment?

Respuesta :

Based on the cost of the flowers and the number of years Joe DiMaggio was expected to live, the present value of the commitment was $2,389.26.

How much is the present value of the commitment?

First convert the interest and period to weekly figures:

Period:

= 52 x 30

= 1,560 weeks

Interest:

= 10.4% / 52

= 0.2% weekly

The present value will be that of an annuity because the amount is constant every week:

= Amount x (1 - (1 + rate) ^ -number of periods) / rate

= 5 x (1 - ( 1 + 0.2%) ⁻¹⁵⁶⁰) / 0.2%

= $2,389.26

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