mohal is going to invest $830 and leave it in an account for 8 years. assuming the interest is compounded…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula when compounded $n$ times a year is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years. Since it is compounded daily, $n = 365$, $P=830$, $A = 1110$, and $t = 8$. So, $1110=830(1 +\frac{r}{365})^{365\times8}$.

Step2: Isolate the exponential term

First, divide both sides of the equation by 830: $\frac{1110}{830}=(1 +\frac{r}{365})^{2920}$. $1.337349=(1 +\frac{r}{365})^{2920}$.

Step3: Take the 2920 - th root of both sides

$1.337349^{\frac{1}{2920}}=1+\frac{r}{365}$. Using a calculator, $1.337349^{\frac{1}{2920}}\approx1.337349^{0.000342466}\approx1.0001017$. So, $1.0001017=1+\frac{r}{365}$.

Step4: Solve for $r$

Subtract 1 from both sides: $1.0001017−1=\frac{r}{365}$. $0.0001017=\frac{r}{365}$. Multiply both sides by 365: $r=0.0001017\times365$. $r = 0.0371205$.

Step5: Convert $r$ to a percentage

To convert $r$ to a percentage, multiply by 100: $r = 3.71205%\approx3.71%$.

Answer:

$3.71%$