Exercise


ABy Admin
Nov 18'23

Answer

Solution: D

The initial level monthly payment is

[[math]] R=\frac{400,000}{a_{\overline{15 \times 12}|0.09/12}}=\frac{400,000}{a_{\overline{180}|0.075}}=4,057.07. [[/math]]

The outstanding loan balance after the 36th payment is

[[math]] B_{3\mathrm{6}}=R a_{\overline{{{160-36}}}|0.0075}=4,057.07a_{\overline{{{144}}}|0.0075}=4,057.07(87.8711)=356,499.17. [[/math]]

The revised payment is 4,057.07 – 409.88 = 3,647.19. Thus,

[[math]] \begin{array}{l}{{356,{499}.17=3,647.19 a_{\overline{144}|j/12}}}\\ {{a_{\overline{144}|j/12}=356,499.17/3,647.19=97.7463.}}\end{array} [[/math]]

Using the financial calculator, j/12 = 0.575%, for j = 6.9%.

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

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