Joe plans on going to Cal Tech. He will need to pay 4 payments of $50,000 when he goes there. In order to do this he will deposit x into an account every month that earns 8% interest convertible monthly for 7 years. He will take out the payments at the end of the last 4 years at the end of the year. After the last withdrawal the account will be exhausted. Calculate x.

• $2,084.95
• $2,016.80
• $2,019.78
• $3,534.01
• $1,999.60

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Solution: B

Deposits: x at 8% convertible monthly = .0067 every month

Withdrawals: 50,000 at months 48, 60, 72, 84

[[math]] \begin{aligned} & X s_{\overline{84}|.0067}-50,000(1.0067)^{36}-50,000(1.0067)^{24} \\ & \quad-50,000(1.0067)^{12}-50,000=0 \\ & X s_{\overline{84} |.0067}=226,450.1209 \\ & \left.X\left[(1.0067)^{84}-1\right) / .0067\right]=226,450.1209\end{aligned} [[/math]]

X = 2016.80

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.