select the correct answer. calculate the compound amount. round to the nearest cent for, p = $1700, r = 9%…

select the correct answer. calculate the compound amount. round to the nearest cent for, p = $1700, r = 9%, compounded semiannually, t = 3 yrs.\n(a) $2213.84\n(b) $2213.85\n(c) $2213.86\n(d) 2213.48

select the correct answer. calculate the compound amount. round to the nearest cent for, p = $1700, r = 9%, compounded semiannually, t = 3 yrs.\n(a) $2213.84\n(b) $2213.85\n(c) $2213.86\n(d) 2213.48

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P=$1700$, $r = 0.09$ (since $9%=0.09$), $n = 2$ (compounded semiannually), and $t = 3$.

Step2: Substitute values into the formula

$A=1700(1 +\frac{0.09}{2})^{2\times3}=1700(1 + 0.045)^{6}$. First, calculate $(1 + 0.045)^{6}$. $(1 + 0.045)^{6}=1.045^{6}\approx1.30226$. Then, $A = 1700\times1.30226=$2213.842$.

Step3: Round to the nearest cent

Rounding $2213.842$ to the nearest cent gives $$2213.84$.

Answer:

A. $2213.84$