monika invests in a real - estate project that earns 6.5% compounded semiannually. if monikas initial…

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 form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P=$10000$, $r = 0.065$, $n = 2$ (semi - annual compounding), and $t = 8$.

Step2: Calculate the amount $A$

Substitute the values into the formula: [ \begin{align*} A&=10000(1 +\frac{0.065}{2})^{2\times8}\ &=10000(1+ 0.0325)^{16}\ &=10000\times(1.0325)^{16} \end{align*} ] Using a calculator, $(1.0325)^{16}\approx1.677008$. So, $A = 10000\times1.677008=$16770.08$.

Step3: Calculate the interest $I$

The interest $I$ is the difference between the final amount $A$ and the principal $P$. So, $I=A - P$. [ \begin{align*} I&=16770.08- 10000\ &=$6770.08 \end{align*} ]

Answer:

$6770.08$