Compound Interest activity - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

The formula used for all these problems is:
Amount ($A$) = Principal ($P$) $\times (1 + \text{rate})^{\text{time}}$
Interest ($I$) = Amount ($A$) - Principal ($P$)

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Part A

1) Principal = \$9,400 | Time = 4 years | Rate = 6%
* Step 1: Convert rate to decimal: $0.06$. Add 1: $1.06$.
* Step 2: Raise to power of time: $1.06^4 \approx 1.262477$.
* Step 3: Multiply by Principal: $9,400 \times 1.262477 \approx 11,867.28$.
* Step 4: Find Interest: $11,867.28 - 9,400 = 2,467.28$.

2) Principal = \$12,900 | Time = 2 years | Rate = 13%
* Step 1: Convert rate to decimal: $0.13$. Add 1: $1.13$.
* Step 2: Raise to power of time: $1.13^2 = 1.2769$.
* Step 3: Multiply by Principal: $12,900 \times 1.2769 = 16,472.01$.
* Step 4: Find Interest: $16,472.01 - 12,900 = 3,572.01$.

3) Principal = \$800 | Time = 9 years | Rate = 4%
* Step 1: Convert rate to decimal: $0.04$. Add 1: $1.04$.
* Step 2: Raise to power of time: $1.04^9 \approx 1.42331$.
* Step 3: Multiply by Principal: $800 \times 1.42331 \approx 1,138.65$.
* Step 4: Find Interest: $1,138.65 - 800 = 338.65$.

4) Principal = \$4,125 | Time = 5 years | Rate = 7%
* Step 1: Convert rate to decimal: $0.07$. Add 1: $1.07$.
* Step 2: Raise to power of time: $1.07^5 \approx 1.40255$.
* Step 3: Multiply by Principal: $4,125 \times 1.40255 \approx 5,785.53$.
* Step 4: Find Interest: $5,785.53 - 4,125 = 1,660.53$.

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Part B

Principal = \$300 | Time = 8 years

a) Rate = 9%
* Step 1: $1 + 0.09 = 1.09$.
* Step 2: $1.09^8 \approx 1.99256$.
* Step 3: $300 \times 1.99256 \approx 597.77$.

b) Rate = 11%
* Step 1: $1 + 0.11 = 1.11$.
* Step 2: $1.11^8 \approx 2.30454$.
* Step 3: $300 \times 2.30454 \approx 691.36$.

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Final Answer:

A)
1) A = \$11,867.28, I = \$2,467.28
2) A = \$16,472.01, I = \$3,572.01
3) A = \$1,138.65, I = \$338.65
4) A = \$5,785.53, I = \$1,660.53

B)
a) \$597.77
b) \$691.36