Revision as of 00:41, 19 November 2023 by Admin (Created page with "Jennifer establishes an investment account to pay for college expenses for her daughter. She plans to invest X at the beginning of each month for the next 21 years. Beginning at the end of the 18th year, she will withdraw 20,000 annually. The final withdrawal at the end of the 21st year will exhaust the account. She anticipates earning an annual effective yield of 8% on the investment. Calculate X. <ul class="mw-excansopts"><li>137.90</li><li>142.80</li><li>146.40</li>...")
ABy Admin
Nov 19'23
Exercise
Jennifer establishes an investment account to pay for college expenses for her daughter. She plans to invest X at the beginning of each month for the next 21 years. Beginning at the end of the 18th year, she will withdraw 20,000 annually. The final withdrawal at the end of the 21st year will exhaust the account. She anticipates earning an annual effective yield of 8% on the investment.
Calculate X.
- 137.90
- 142.80
- 146.40
- 150.60
- 154.30
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: B
The monthly interest rate is
[[math]]
j = (1.08)^{1/12}-1 = 0.643\%.
[[/math]]
Then,
[[math]]
20.000S_{\overline{3}|0.08}=X \ddot{s}_{\overline{252}|0.00643}\quad90,122.24=630.99X,\quad X=142.83.
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.