Question

What interest rate would be necessary to obtain $6,500 in 8 years if $5,000 is the amount of the original investment and the interest is compounded yearly?

Answer 1

The formular is

$A=P(1+\frac{r}{n})^{nt}$$6500=5000(1+\frac{r}{1})^{1\times8}$$\frac{6500}{5000}=(1+r)^8$$1.3=(1+r)^8$$1.3^{\frac{1}{8}}=(1+r)^{8\times\frac{1}{8}}$$1.3^{0.125}=1+r$$1.0333=\text{ 1+r}$

subtract 1 from bothside

$r\text{ = 0.0333}$

R = 0.0333 x 100% = 3.33%