Revision as of 21:50, 17 November 2023 by Admin (Created page with "Eric’s (compound) interest in the last 6 months of the 8th year is <math>100(1 + \frac{i}{2})^{15} \frac{i}{2}</math>. Mike’s (simple) interest for the same period is <math>200 \frac{i}{2}</math>. Thus <math display="block"> \begin{align*} \left(1+{\frac{i}{2}}\right)^{\frac{5}{2}}{\frac{i}{2}} &= 200\frac{i}{2} \\ \left(1+{\frac{i}{2}}\right)^{\frac{15}{2}} &= 2 \\ 1+\frac{i}{2} &=1.04739 \\ i =0.09459 &=9.46\%. \end{align*} </math> {{soacopyright | 2023 }}")
Exercise
ABy Admin
Nov 17'23
Answer
Eric’s (compound) interest in the last 6 months of the 8th year is [math]100(1 + \frac{i}{2})^{15} \frac{i}{2}[/math].
Mike’s (simple) interest for the same period is [math]200 \frac{i}{2}[/math].
Thus
[[math]]
\begin{align*}
\left(1+{\frac{i}{2}}\right)^{\frac{5}{2}}{\frac{i}{2}} &= 200\frac{i}{2} \\
\left(1+{\frac{i}{2}}\right)^{\frac{15}{2}} &= 2 \\
1+\frac{i}{2} &=1.04739 \\
i =0.09459 &=9.46\%.
\end{align*}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.