Mat takes out a loan for a car for $35,000. He must make 16 annual payments of $4,000. For the first 7 years the interest rate is 8%, what is the annual effective interest rate for the last 9 years?

• .115
• .242
• .082
• .087
• .468

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

Solution: D

pv = 35000, i = .08 for first 7 years

[[math]] \begin{aligned} & 35000=4000\left[\mathrm{a}_{\overline{7}|0.08}+\mathrm{v}_{.08}{ }^7 \mathrm{a}_{\overline{9} \mid \mathrm{x}}\right] \\ & 8.75=\mathrm{a}_{\overline{7}|0.08}+\mathrm{v}_{.08} \mathrm{a}_{\overline{9} \mid \mathrm{x}} \\ & 6.073=\mathrm{a}_{\overline{9} \mid \mathrm{x}} \\ & \mathrm{i}=.0868\end{aligned} [[/math]]

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