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.

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.