find the accumulated value of an investment of $20,000 for 5 years at an interest rate of 15% if the money…

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), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Given $P=$20000$, $r = 0.15$, $t = 5$ years, and for semi - annual compounding $n = 2$.

Step2: Substitute values into the formula

$A=20000(1 +\frac{0.15}{2})^{2\times5}$ First, calculate the value inside the parentheses: $\frac{0.15}{2}=0.075$, then $1 + 0.075=1.075$. And $2\times5 = 10$. So $A = 20000\times(1.075)^{10}$.

Step3: Calculate $(1.075)^{10}$

Using a calculator, $(1.075)^{10}\approx2.061032$.

Step4: Calculate the final amount

$A=20000\times2.061032=$41220.64$

Answer:

$41220.64$