Question

What interest rate, compounded semiannually, results in an annual effective rate of 6%? Input your answer as a percentage rounded to two decimal places.

Answer 1

The relation between anual interest and semiannual compounded interest is:

$\begin{gathered} \text{annal interest=y, semiannual interest=x} \\ (1+y)=(1+x)^2 \end{gathered}$

In this case, the annula interest is 6%=0.06, so:

$\begin{gathered} 1+0.06=(1+x)^2 \\ 1+x=\sqrt[]{1.06} \\ x=\sqrt[]{1.06}-1=0.02956 \end{gathered}$

So the semiannual interest rate is 2.95%