A 5-year loan of 500,000 with an annual effective discount rate of 8% is to be repaid by level end-of-year payments.

If the first four payments had been rounded up to the next multiple of 1,000, the final payment would be X.

Calculate X.

• 103,500
• 111,700
• 115,200
• 125,200
• 127,500

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

Solution: D

The annual effective interest rate is 0.08/(1 – 0.08) = 0.08696.

[[math]] 500,000/a_{\overline{5}|0.08696}=500,000/3.9205=127,535. [[/math]]

This rounds up to 128,000. The equation of value for X is

[[math]] \begin{array}{l}{{128,000a_{\overline{{{4}}}|{0.08696}}+X(1.08696)^{-5}=500,000}}\\ {{X=(500,000-417,466.36)(1.51729)=125,227.}}\end{array} [[/math]]

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