find the accumulated value of an investment of $15,000 for 6 years at an interest rate of 1.15% if the money…

Explanation:

Step1: Identify the 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. Given $P=$15000$, $r = 0.0115$, $t = 6$ years, and when compounded semiannually $n = 2$.

Step2: Substitute the values into the formula

$A=15000(1 +\frac{0.0115}{2})^{2\times6}$ First, calculate the value inside the parentheses: $\frac{0.0115}{2}=0.00575$, then $1+\frac{0.0115}{2}=1 + 0.00575=1.00575$. Next, calculate the exponent: $2\times6 = 12$. So, $A = 15000\times(1.00575)^{12}$.

Step3: Calculate $(1.00575)^{12}$

Using a calculator, $(1.00575)^{12}\approx1.071177$.

Step4: Calculate the accumulated value $A$

$A=15000\times1.071177 = 16067.655\approx16067.66$

Answer:

$16067.66$