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Your client is 144 years old
Your client is 144 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $19800 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 10% in the future. a) If she follows your advice, how much money will she have at 183? (15 point) b) How much will she have at 188? (1.5 point) C) She expects to live for 20 years if she retires at 183 and for 15 years if she retires at 188. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age? (3 point)
Expert Solution
a)
Number of periods = 183 - 144 = 39
Future value = Annuity * [(1 + rate)^periods] / rate
Future value = 19,800 * [(1 + 0.1)^39 - 1] / 0.1
Future value = 19,800 * [41.14478 - 1] / 0.1
Future value = 19,800 * 401.44778
Future value = $7,948,666.00
She will have $7,948,666.00
b)
Number of periods = 188 - 144 = 44
Future value = Annuity * [(1 + rate)^periods] / rate
Future value = 19,800 * [(1 + 0.1)^44 - 1] / 0.1
Future value = 19,800 * [66.26408 - 1] / 0.1
Future value = 19,800 * 652.64076
Future value = $12,922,287.06
She will have $12,922,287.06
c)
Retires at 183:
Present value = Annuity * [1 - 1 / (1 + rate)^periods] / rate
7,948,666.00 = Annuity * [1 - 1 / (1 + 0.1)^20] / 0.1
7,948,666.00 = Annuity * [1 - 0.14864] / 0.1
7,948,666.00 = Annuity * 8.51356
Annuity = $933,647.33
She will be able to withdraw $933,647.33
Retires at 188:
Present value = Annuity * [1 - 1 / (1 + rate)^periods] / rate
12,922,287.06 = Annuity * [1 - 1 / (1 + 0.1)^15] / 0.1
12,922,287.06 = Annuity * [1 - 0.23939] / 0.1
12,922,287.06 = Annuity * 7.60608
Annuity = $1,698,941.78
She will be able to withdraw $1,698,941.89
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