Revision as of 12:21, 19 November 2023 by Admin (Created page with "'''Solution: D''' Amount of loan = L Initial expected yield rate = 10.00% Annual payment = <math>L/a_{\overline{10}|10\%}</math> Accumulated value at time 10 = <math>L/a_{\overline{10}|10\%})(S_{\overline{4}|10\%}1.07^6 + s_{6|7\%})</math> <math display = "block"> \begin{aligned} \textrm{Yield Rate} = \left(\frac{\textrm{Accum Value}}{L}\right)^{1/10}-1 \\ =\left(\frac{s_{\overline{4}|10\%}+ s_{\overline{6}|7\%}}{a_{\overline{10}|10\%}}\right)^{1/10} - 1 \\ =\left(...")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: D
Amount of loan = L
Initial expected yield rate = 10.00%
Annual payment = [math]L/a_{\overline{10}|10\%}[/math]
Accumulated value at time 10 = [math]L/a_{\overline{10}|10\%})(S_{\overline{4}|10\%}1.07^6 + s_{6|7\%})[/math]
[[math]]
\begin{aligned}
\textrm{Yield Rate} = \left(\frac{\textrm{Accum Value}}{L}\right)^{1/10}-1 \\
=\left(\frac{s_{\overline{4}|10\%}+ s_{\overline{6}|7\%}}{a_{\overline{10}|10\%}}\right)^{1/10} - 1
\\
=\left(\frac{4.6410(1.5007)+7.1533}{6.1446}\right)^{1/10}-1 \\
=8.67\% \\
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.