1. how much money will be in an account if $1600 is invested at 1.7% compounded monthly for 9 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

We have $P=$1600$, $r = 1.7%=0.017$, $n = 12$ (compounded monthly), and $t = 9$ years.

Step3: Substitute the values into the formula

$A=1600(1 +\frac{0.017}{12})^{12\times9}$. First, calculate the value inside the parentheses: $\frac{0.017}{12}\approx0.0014167$, then $1+\frac{0.017}{12}=1 + 0.0014167=1.0014167$. Next, calculate the exponent: $12\times9 = 108$. So, $A = 1600\times(1.0014167)^{108}$. Using a calculator, $(1.0014167)^{108}\approx1.16377$. Then $A=1600\times1.16377=$1862.032$.

Answer:

$$1862.03$ (rounded to the nearest cent)