Chapter 5.7, Problem 28AYU

In Problems 27-30, determine the rate that represents the better deal.

$9\%$ compounded quarterly or $9\frac{1}{4}\%$ compounded annually

To determine

To find: The rate that represents the better deal.

$\text{9\%}$ compounded quarterly or $9\frac{1}{4}\%$ compounded annually

Answer to Problem 28AYU

Solution:

$9\%$ Compounded quarterly is the best deal.

Explanation of Solution

Given:

$r=9\%=0.09n=4$ (quarterly compounding) and $r=9\frac{1}{4}\%=0.0925, n=1$ (yearly compounding)

Calculation:

For $r=9\%=0.09n=4$

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

$={\left(1+\frac{0.09}{4}\right)}^4-1$

$=0.09308$

$=9.308\%$

$r=9\frac{1}{4}\%=0.0925, n=1$

$r_e=9.25\%$

$9\%$ Compounded quarterly is the best deal.