an initial investment amount p, an annual interest rate r, and a time t are given. find the future - value…

Explanation:

Step1: Recall compound - interest formula for monthly compounding

The formula for compound interest when compounded $n$ times a year is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years. For monthly compounding, $n = 12$. Given $P=$115000$, $r = 0.032$, and $t = 6$.

Step2: Substitute the values into the formula

$A=115000(1 +\frac{0.032}{12})^{12\times6}$. First, calculate the value inside the parentheses: $\frac{0.032}{12}\approx0.002667$, then $1+\frac{0.032}{12}=1.002667$. Next, calculate the exponent: $12\times6 = 72$. So, $A = 115000\times(1.002667)^{72}$.

Step3: Calculate $(1.002667)^{72}$

Using a calculator, $(1.002667)^{72}\approx1.21037$.

Step4: Calculate the future - value $A$

$A=115000\times1.21037=$139192.55$.

Answer:

$139192.55$