how much interest will be earned on a $1800 investment at 6.41% compounded quarterly for 6 years? state your…

Explanation:

Step1: Identify the compound - interest formula

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 form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. The interest earned $I=A - P$. Here, $P = 1800$, $r=0.0641$, $n = 4$ (compounded quarterly), and $t = 6$.

Step2: Calculate the value of $(1+\frac{r}{n})^{nt}$

First, calculate $\frac{r}{n}=\frac{0.0641}{4}=0.016025$. Then, $nt=4\times6 = 24$. So, $(1+\frac{r}{n})^{nt}=(1 + 0.016025)^{24}$. Using a calculator, $(1.016025)^{24}\approx1.46977$.

Step3: Calculate the amount $A$

$A=P(1+\frac{r}{n})^{nt}=1800\times1.46977 = 2645.586$.

Step4: Calculate the interest $I$

$I=A - P=2645.586-1800=845.586\approx845.59$.

Answer:

845.59