how much interest will be earned on a $2200 investment at 6.88% compounded quarterly for 8 years? state your…

how much interest will be earned on a $2200 investment at 6.88% compounded quarterly for 8 years? state your answer in terms of dollars, rounded to the nearest cent, but do not include a $ sign or the word \dollars\ with your response.

how much interest will be earned on a $2200 investment at 6.88% compounded quarterly for 8 years? state your answer in terms of dollars, rounded to the nearest cent, but do not include a $ sign or the word \dollars\ with your response.

Answer

Explanation:

Step1: Identify compound - interest formula components

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P=$2200$, $r = 0.0688$, $n = 4$ (compounded quarterly), and $t = 8$. First, calculate $(1+\frac{r}{n})^{nt}$. $(1+\frac{0.0688}{4})^{4\times8}=(1 + 0.0172)^{32}$

Step2: Calculate $(1 + 0.0172)^{32}$

Using a calculator, $(1 + 0.0172)^{32}\approx1.70977$.

Step3: Calculate the final amount $A$

$A=P(1+\frac{r}{n})^{nt}=2200\times1.70977 = 3761.494$.

Step4: Calculate the interest earned

The interest earned $I=A - P$. So, $I=3761.494−2200=1561.494\approx1561.49$.

Answer:

1561.49