Mason receives $23,000 from a life insurance policy. He uses the fund to purchase different annuities, each costing $11,500. His first annuities is an 18 year annuity-immediate paying K per year. The second annuity is a 7 year annuity paying 2K per year. Both annuities are based on an annual effective interest rate of i, i>0.

Determine i.

• .053
• 2.08
• .052
• .5
• .99

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

Solution: C

PV= 11,500, interest=i

[[math]] \begin{aligned} 11,500 = K a_{\overline{18}|i} = 2Ka_{\overline{7}|i} \\ a_{\overline{18}|i} = a_{\overline{7}|i}\\ i=.052 \end{aligned} [[/math]]

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