Question

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

Answer 1

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

Explanation:

Compound interest is represented by the following equation:

`\begin{gathered} A=P(1+(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+(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}`