Revision as of 01:36, 19 November 2023 by Admin (Created page with "'''Solution: C''' After one year the outstanding balance is <math>500 a_{\left.\overline{48}\right|_{0.025}}=13,886.58</math>. This must match the present value of the revised payments: <math display = "block"> \begin{aligned} & 13,886.58=X v^6 a_{\overline{6}|0.025}+500 v^{12} a_{\overline{36}|0.025}=4.74964 X+8,757.69 \\ & X=(13,886.58-8,757.69) / 4.74964=1,079.85 \end{aligned} </math> Alternatively, each missing payment is being replaced with a larger payment six mo...")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: C
After one year the outstanding balance is [math]500 a_{\left.\overline{48}\right|_{0.025}}=13,886.58[/math]. This must match the present value of the revised payments:
[[math]]
\begin{aligned}
& 13,886.58=X v^6 a_{\overline{6}|0.025}+500 v^{12} a_{\overline{36}|0.025}=4.74964 X+8,757.69 \\
& X=(13,886.58-8,757.69) / 4.74964=1,079.85
\end{aligned}
[[/math]]
Alternatively, each missing payment is being replaced with a larger payment six months later. The larger payment should be the payment due plus the missed payment with interest, or [math]500+500(1.025)^6=1,079.85[/math]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.