Revision as of 00:38, 19 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>103,500</li><li>111,700</li><li>115,200</li><li>125,200</li><li>127,500</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
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.
ABy Admin
Nov 19'23
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.