suppose that $2000 is loaned at a rate of 16.5%, compounded semiannually. assuming that no payments are…

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 or borrowed for in years.

Step2: Convert given values to appropriate form

The principal $P=$2000$, the annual interest rate $r = 16.5%=0.165$, the number of times compounded per year $n = 2$ (since it's compounded semiannually), and the time $t = 5$ years.

Step3: Substitute values into the formula

$A=2000(1 +\frac{0.165}{2})^{2\times5}$. First, calculate the value inside the parentheses: $\frac{0.165}{2}=0.0825$, then $1+\frac{0.165}{2}=1 + 0.0825=1.0825$. Next, calculate the exponent: $2\times5 = 10$. So, $A = 2000\times(1.0825)^{10}$.

Step4: Calculate the final amount

$(1.0825)^{10}\approx2.172977$. Then $A=2000\times2.172977 = 4345.954$. Rounding to the nearest cent, $A\approx$4345.95$.

Answer:

$4345.95$