you deposit $3000 in an account earning 3% interest compounded monthly. how much will you have in the…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert values to appropriate form

The principal $P=$3000$, the annual interest rate $r = 3%=0.03$, the number of times compounded per year $n = 12$ (monthly compounding), and the time $t = 5$ years.

Step3: Substitute values into the formula

$A=3000(1 +\frac{0.03}{12})^{12\times5}$. First, calculate $\frac{0.03}{12}=0.0025$. Then $1+\frac{0.03}{12}=1 + 0.0025=1.0025$. And $12\times5 = 60$. So $A = 3000\times(1.0025)^{60}$.

Step4: Calculate $(1.0025)^{60}$

Using a calculator, $(1.0025)^{60}\approx1.16161678$.

Step5: Calculate the final amount $A$

$A=3000\times1.16161678\approx3484.85$.

Answer:

$3484.85$