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ABy Admin
Nov 19'23
Exercise
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.
ABy Admin
Nov 19'23
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.