how much will $3,500 deposited in an account earning 6.7% interest compounded monthly be worth in 17 years…

Explanation:

Step1: Identify the 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 the given values to the appropriate form

Given $P=$3500$, $r = 6.7%=0.067$, $n = 12$ (compounded monthly), and $t = 17$ years.

Step3: Substitute the values into the formula

$A=3500(1 +\frac{0.067}{12})^{12\times17}$. First, calculate the value inside the parentheses: $\frac{0.067}{12}\approx0.0055833$, then $1+\frac{0.067}{12}=1 + 0.0055833=1.0055833$. Next, calculate the exponent: $12\times17 = 204$. So, $A = 3500\times(1.0055833)^{204}$.

Step4: Calculate the final amount

$(1.0055833)^{204}\approx3.17777$. Then $A=3500\times3.17777=$11122.195\approx$11122.20$.

Answer:

$11122.20$