Question

What rate of interest compounded quarterly will yield an effective interest rate of 5 %?

Answer 1

If the effective yearly interest rate is 5%, the amount at the end of one year is the principal multiplied by 1.05.
Let the yearly interest rate compounded quarterly be r. Then we can write the equation:
\[\large (1+\frac{r}{4})^{4}=1.05\ ..........(1)\]
Taking the fourth root of both sides of (1) we get:
\[\large 1+\frac{r}{4}=\sqrt[4]{1.05}\ ........(2)\]
which can be rearranged to give:
\[\large r=4(\sqrt[4]{1.05}-1)=you\ can\ calculate\]

Answer 2

Thank you, I got 12.40%

Answer 3

Or 12.395% because it wants it rounded to 3 decimal places

Answer 4

Unfortunately your result is way too large. Please post the steps in your calculation.

Answer 5

I did it again and got .049. Not sure if that is any better though

Answer 6

That is correct. To convert to a percentage multiply by 100:
\[\large Percentage\ rate=0.049\times100=(you\ can\ calculate)\ percent\]