Revision as of 00:22, 19 November 2023 by Admin (Created page with "'''Solution: D''' The amount of the loan is the present value of the deferred increasing annuity: <math display = "block"> (1.05)^{-10}\left[500\ddot{a}_{\overline{{{300}}}|0.05}+500(I\ddot{a})_{\overline{{{300}}}|0.05}\right] = (1.05^{-10})(500)\Bigg[\ddot{a}_{\overline{{{300}}}|0.05}+\frac{\ddot{a}_{\overline{{{300}}}|0.05}-30(1.05)^{-30}}{0.05/1.05}\Bigg]=64,257. </math> {{soacopyright | 2023 }}")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: D
The amount of the loan is the present value of the deferred increasing annuity:
[[math]]
(1.05)^{-10}\left[500\ddot{a}_{\overline{{{300}}}|0.05}+500(I\ddot{a})_{\overline{{{300}}}|0.05}\right] = (1.05^{-10})(500)\Bigg[\ddot{a}_{\overline{{{300}}}|0.05}+\frac{\ddot{a}_{\overline{{{300}}}|0.05}-30(1.05)^{-30}}{0.05/1.05}\Bigg]=64,257.
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.