Chapter 5.7, Problem 37AYU

What rate of interest compounded quarterly will yield an effective interest rate of $7\%$?

To determine

To find: What rate of interest compounded quarterly will yield an effective interest rate of $\text{7\%}$?

Answer to Problem 37AYU

Solution:

$\text{6}\text{.823\%}$ is rate of interest compounded quarterly will yield an effective interest rate of $\text{7\%}$.

Explanation of Solution

Given:

$r_e=7\%=0.07n=4$(quarterly compounding)

Calculation:

$r_e= {\left(1+\frac{r}{n}\right)}^n-1$

$0.07={\left(1+\frac{r}{4}\right)}^4-1$

$0.07+1={\left(\frac{4+r}{4}\right)}^4$

$\frac{{\left(4+r\right)}^4}{256}=1.07$

${\left(4+r\right)}^4=273.92$

$4+r={\left(273.92\right)}^{\frac{1}{4}}$

$4+r=4.06823$

$r=0.06823$

$r=6.823\%$