Jeffery invests $4,000 at an annual effective rate of 7%. The interest is paid every year and Jeffery reinvests it at annual rate i. At the end of 12 years the accumulated interest is $7,500.

If Jane invests $1,000 at the end of each year for 25 years at a rate of interest of 10%, and she reinvests his interest that is paid annually into an account at an effective rate of I, what is Jane’s accumulated interest at the end of 25 years?

• $108,415.03
• $125,777.77
• $54,641.48
• $77,990.75
• $123,276.77

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

Solution: A

We first need to calculate Jeffery’s accumulated interest at the end of each 12 years. His interest each year is: 4000(.07) = 280, so:

[[math]] \begin{aligned} 280s_{\overline{12}|i} = 7500 \\ s_{\overline{12}|i} = 26.786 \\ i = .137 \end{aligned} [[/math]]

Jane’s interest would be:

1000(.1) = 100 at the end of 2nd year

2000(.1) = 200 or 2(100) at the end of 3rd year

3000(.1) = 300 or 3(100) at the end of 4th year

. . .

24000(.1) = 2400 or 24(100) at the end of 25th year

Which is a 25 year increasing annuity. She puts this money into an account with interest i

[[math]] 100(Is)_{\overline{24}|.137} = 100(1084.15029) =108,415.03. [[/math]]

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