an investment of $7,000 at 1% is compounded semiannually for three years. find the future value and compound…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula for compounding $n$ 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 form), $n$ is the number of times compounded per year, and $t$ is the number of years. Here, $P=$7000$, $r = 0.01$ (since $1%=0.01$), $n = 2$ (semi - annual compounding), and $t = 3$ years.

Step2: Substitute the values into the formula

$A=7000(1 +\frac{0.01}{2})^{2\times3}=7000(1 + 0.005)^{6}$. First, calculate $(1 + 0.005)^{6}$. Using a calculator, $(1.005)^{6}\approx1.0303775$. Then, $A = 7000\times1.0303775=$7212.6425$.

Step3: Calculate the compound interest

The compound interest $CI=A - P$. So, $CI=7212.6425−7000=$212.6425$.

Answer:

The future value of the investment is $$7212.64$