Revision as of 22:57, 17 November 2023 by Admin (Created page with "A corporation makes a payment at the end of each month into a savings account that offers an annual nominal interest rate of 8% compounded quarterly. Determine the equivalent effective rate of interest per payment period. <ul class="mw-excansopts"><li>(1 + 8%/4)<sup>1/3</sup>-1</li><li>(1 + 8%/12)-1</li><li>(1 + 8%/12)<sup>3</sup>-1</li><li>(1 + 8%/12)<sup>1/12</sup>-1</li><li>(1 + 8%/4)<sup>4</sup>-1</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 17'23
Exercise
A corporation makes a payment at the end of each month into a savings account that offers an annual nominal interest rate of 8% compounded quarterly.
Determine the equivalent effective rate of interest per payment period.
- (1 + 8%/4)1/3-1
- (1 + 8%/12)-1
- (1 + 8%/12)3-1
- (1 + 8%/12)1/12-1
- (1 + 8%/4)4-1
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 17'23
Solution: A
We are given [math]i^{(4)}=8\%[/math] and want to determine [math]i^{(12)}/12[/math].The equation that links the two and its solution is:
[[math]]
\begin{aligned}
\left(1+\frac{i^{(12)}}{12}\right)^{12}=\left(1+\frac{i^{(4)}}{4}\right)^{4}=\left(1+\frac{8\%}{4}\right)^{4} \\
\left(1+\frac{i^{(12)}}{12}\right)=\left(1+\frac{8\%}{4}\right)^{4/12} \\
\frac{i^{(12)}}{12}=\left(1+\frac{8\%}{4}\right)^{1/3}-1
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.