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.

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.