Problem
$8000 accumulating to $11672.12 compounded quarterly for 8 years. Find the interest rate for each deposit and compound amount.
Solution
For this case we need to apply the compound interest formula given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where A= 11672.12 represent the future value
P= 8000 represent the present value
n= 4 since the rate is compounded quarterly
t= 8 years
And we need to solve for r. So we can begin doing this:
[tex]11672.12=8000(1+\frac{r}{4})^{8\cdot4}[/tex][tex]\frac{11672.12}{8000}=(1+\frac{r}{4})^{32}[/tex]We have this:
[tex](\frac{11672.12}{8000})^{\frac{1}{32}}=1+\frac{r}{4}[/tex]And solving for r we have:
r= 4*[(11672.12/8000)^(1/32) -1]
And doing the math we got:
r= 0.0475
And this rate correspond to r= 4.75 %
