Revision as of 23:50, 18 November 2023 by Admin (Created page with "A loan of 20,000 is repaid by a payment of X at the end of each year for 10 years. The loan has an annual effective interest rate of 11% for the first five years and 12% thereafter. Calculate X. <ul class="mw-excansopts"><li>2739.5</li><li>3078.5</li><li>3427.5</li><li>3467.5</li><li>3484.5</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
A loan of 20,000 is repaid by a payment of X at the end of each year for 10 years. The loan has an annual effective interest rate of 11% for the first five years and 12% thereafter.
Calculate X.
- 2739.5
- 3078.5
- 3427.5
- 3467.5
- 3484.5
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: C
[[math]]
\begin{array}{l}{{20.000=X\left(a_{\overline{5}|0.11}+1.11^{-5}a_{\overline{5}|0.12}\right)=X(3.69590+3.60478/1.68506)=5.83516\,X}}\\ {{\mathrm{X=20.000}/5.83516=3427.50.}}
\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.