Revision as of 22:52, 17 November 2023 by Admin (Created page with "An investor deposits 100 into a bank account at time 0. The bank credits interest at an annual nominal interest rate of i, compounded semi-annually. The total amount of interest credited in the twelfth year is twice the amount of interest credited in the fifth year. Calculate i. <ul class="mw-excansopts"><li>10.15%</li><li>10.24%</li><li>10.32%</li><li>10.41%</li><li>10.48%</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 17'23
Exercise
An investor deposits 100 into a bank account at time 0. The bank credits interest at an annual nominal interest rate of i, compounded semi-annually. The total amount of interest credited in the twelfth year is twice the amount of interest credited in the fifth year.
Calculate i.
- 10.15%
- 10.24%
- 10.32%
- 10.41%
- 10.48%
ABy Admin
Nov 17'23
Solution: A
[[math]]
\begin{align*}
1{\mathrm{00}}{\bigg(}1+{\frac{i}{2}}{\bigg)}^{22}\left[\left(1+{\frac{i}{2}}\right)^{2}-1\right]=2{\bigg(}1{\mathrm00}{\bigg)}{\bigg(}1+{\frac{i}{2}}{\bigg)}^{8}\left[{\bigg(}1+{\frac{i}{2}}{\bigg)}^{2}-1\right] \\
2=(1+i)^{14}\\
i = (2^{1/14}-1)2 = 0.1015 = 10.15\%.
\end{align*}
[[/math]]