find the accumulated value of an investment of $15,000 for 7 years at an interest rate of 1.45% 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, $t$ is the number of years, and $A$ is the accumulated amount. Given $P=$15000$, $r = 0.0145$, $t = 7$ years. When compounded semiannually, $n = 2$.

Step2: Substitute the values into the formula

$A=15000(1 +\frac{0.0145}{2})^{2\times7}$ First, calculate the value inside the parentheses: $\frac{0.0145}{2}=0.00725$, then $1+\frac{0.0145}{2}=1 + 0.00725=1.00725$. And $2\times7 = 14$. So $A = 15000\times(1.00725)^{14}$.

Step3: Calculate $(1.00725)^{14}$

Using a calculator, $(1.00725)^{14}\approx1.107777$.

Step4: Calculate the accumulated value $A$

$A=15000\times1.107777=$16616.66$

Answer:

$16616.66$