Question

Find the interest earned given the following:Amount needed: $269,000Time in years: 6Interest: 8%Compounded: semiannually

Answer 1

Answer:

$I=\text{ \ }161,678$

Step-by-step explanation:

Compound interest is represented by the following equation:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ P=\text{ principal amount invested} \\ r=\text{ interest rate} \\ n=\text{ times compounded per unit ''t''} \\ t=\text{ time in years} \end{gathered}$

Therefore, for the given information:

$A=269,000\cdot(1+\frac{0.08}{2})^{12}$

Solve for the future amount, and then subtract it from the principal. The product would be the interest earned:

$\begin{gathered} A=430,678 \\ \text{Hence,} \\ I=A-P \\ I=430678-269000 \\ I=\text{ \ }161,678 \end{gathered}$