A 20-year loan of 500 based on a 5% annual effective interest rate is repaid with level installments at the end of each year.

Determine the installment in which the principal and interest portions are most nearly equal to each other.

• 1st
• 7th
• 10th
• 13th
• 20th

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

[[math]] \begin{aligned} & P_t=I_t \\ & v^{20-t+1}=\left(1-v^{20-t+1}\right) \\ & 2 v^{20-t+1}=1 \\ & v^{21-t}=0.5 \\ & 1.05^{21-t}=2 \\ & (21-t) \ln (1.05)=\ln 2 \\ & t=7\end{aligned} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.