Question

Lester hopes to earn $1100 in interest in 1.5 years time from $22,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds quarterly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be

Answer 1

Answer:

The answer is "3.27%"

Explanation:

$P = \ 22,000\\\\t = 1.5\\\\I= \ 1,100\\\\A=P+I=\ 22,000+1,100=\ 23,100\\\\n = 4$

Using formula:

$\bold{A=P(1+\frac{r}{n})^{nt}}$

$23,100=22,000(1+\frac{r}{4})^{4\times 1.5}\\\\23,100=22,000(1+\frac{r}{4})^{6}\\\\\frac{23,100}{22,000}=(1+\frac{r}{4})^{6}\\\\1.05=(1+\frac{r}{4})^{6}\\\\1.05^{\frac{1}{6}}=(1+\frac{r}{4})\\\\1.008164846=(1+\frac{r}{4})\\\\1.008164846-1=\frac{r}{4}\\\\0.008164846=\frac{r}{4}\\\\r=0.008164846\times 4\\\\r=0.03266\\\\r=3.266\% \approx 3.27\%$