Question

In the following problems, find (a) the compound amount and (b) the compound interest for the given investment and annual rate. 1. $4,000 for 7 years at 6% compounded annually. 2. $5,000 for 20 years at 5% compounded annually. 3. $700 for 15 years at 7% compounded semiannually.

Answer 1

Explanation:

The compound interest is represented by the following equation:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \text{where}, \\ A=\text{ compound interest} \\ P=\text{ principal} \\ r=\text{ interest rate} \\ t=\text{time} \\ n=\text{times per year compounded} \end{gathered}`

Therefore, for:

1. P=$4,000, t=7 years at r=6%

`\begin{gathered} A=4000(1+0.06)^7 \\ A=\text{ \$6,014.52} \\ \\ \text{For the interest, subtract the principal amount:} \\ I=\text{ \$6,014.52}-\text{ \$4,000} \\ I=\text{ \$2,014.52} \end{gathered}`

2. P= $5,000, t=20 years at r=5%

`\begin{gathered} A=5000(1+0.05)^(20) \\ A=\text{ \$13,266.48} \\ \\ \text{For the interest, subtract the principal amount:} \\ I=\text{ \$13,266.48-\$5,000} \\ I=\text{ \$8,266.48} \end{gathered}`

3. P=$700, t=15 years at 7%, n=2

`\begin{gathered} A=700(1+(0.07)/(2))^15\cdot2 \\ A=1964.75 \\ \\ I=1964.75-700 \\ I=1264.75 \end{gathered}`