Question

What interest rate compounded semiannually will yield an effective interest rate of 6%?

Answer 1

Equate the formula for compound interest with the added interest rate

6% => 0.06

`\begin{gathered} 1+0.06=(1+(r)/(n))^2 \\ 1.06=(1+(r)/(2))^2 \end{gathered}`

Get the square root of both sides.

`\begin{gathered} \sqrt[]{1.06}=\sqrt[]{(1+(r)/(n))^2} \\ \sqrt[]{1.06}=1+(r)/(2) \\ \sqrt[]{1.06}-1=(r)/(2) \\ r=2(\sqrt[]{1.06}-1) \\ r=0.0591260282 \end{gathered}`

Converting the result to percentage, and rounding it off to the nearest tenth of a percent. The rate is 5.9%.