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 $4. Based on actuarial tables, "Joltin' Joe" could expect to live for 37 years after the actress died. Assume that the EAR is 11.4 percent. Also, assume that the price of the flowers will increase at 3.1 percent per year, when expressed as an EAR. Assuming that each year has exactly 52 weeks, what is the present value of this commitment? Joe began purchasing flowers the week after Marilyn died.

Answer 1

Answer:

Given:

EAR = 11.40%

Weekly interest rate = r = (1 + 11.40%) ^ (1/52) - 1 = 0.207825546053741%

Growth rate expressed as EAR = 3.10%

Weekly growth rate = g = (1 + 3.10%) ^ (1/52) - 1 = 0.0587272473817846%

Number of weeks = n = 37 * 52 = 1924

Formula for PV of growing annuity = P / (r - g) * (1 - ((1 + g) / (1 + r)) ^n)

Where r = Periodic interest rate

g= periodic growth rate

n = Number of periods

P = Initial PMT

Hence:

Present value = 4 / ( 0.207825546053741% - 0.0587272473817846%) * (1 - ((1 + 0.0587272473817846%) / (1 + 0.207825546053741%))^1924)

= $2529.89

Present value of this commitment = $2,529.89