Compound Interest worksheet with problems to find interest and amount, suitable for math practice.

Let's solve each part of this Compound Interest worksheet step by step.

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🔷 Formula for Compound Interest (compounded annually):

$$
A = P(1 + r)^t
$$

Where:
- $ A $ = Amount after interest
- $ P $ = Principal (initial amount)
- $ r $ = Annual interest rate (as a decimal)
- $ t $ = Time in years

Then, the compound interest is:

$$
I = A - P
$$

We'll use this formula for all problems.

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## ✔ Part A: Find compound interest (I) and amount (A)

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1) Principal = $9,400, Time = 4 years, Rate = 10% compounded annually

- $ P = 9400 $
- $ r = 10\% = 0.10 $
- $ t = 4 $

$$
A = 9400(1 + 0.10)^4 = 9400(1.10)^4
$$

Calculate $ (1.10)^4 $:

$$
1.10^2 = 1.21 \\
1.10^4 = (1.21)^2 = 1.4641
$$

$$
A = 9400 \times 1.4641 = 13,772.54
$$

Now, find interest:

$$
I = A - P = 13,772.54 - 9,400 = 4,372.54
$$

✔ Answer:
- $ A = \$13,772.54 $
- $ I = \$4,372.54 $

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2) Principal = $12,900, Time = 2 years, Rate = 13% compounded annually

- $ P = 12,900 $
- $ r = 0.13 $
- $ t = 2 $

$$
A = 12,900(1 + 0.13)^2 = 12,900(1.13)^2
$$

$ 1.13^2 = 1.2769 $

$$
A = 12,900 \times 1.2769 = 16,452.01
$$

$$
I = 16,452.01 - 12,900 = 3,552.01
$$

✔ Answer:
- $ A = \$16,452.01 $
- $ I = \$3,552.01 $

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3) Principal = $800, Time = 9 years, Rate = 25% compounded annually

- $ P = 800 $
- $ r = 0.25 $
- $ t = 9 $

$$
A = 800(1 + 0.25)^9 = 800(1.25)^9
$$

Now calculate $ 1.25^9 $. Let's do it step by step:

- $ 1.25^2 = 1.5625 $
- $ 1.25^4 = (1.5625)^2 = 2.44140625 $
- $ 1.25^8 = (2.44140625)^2 ≈ 5.958396 $
- $ 1.25^9 = 5.958396 \times 1.25 ≈ 7.447995 $

So:

$$
A ≈ 800 \times 7.447995 ≈ 5,958.396 → \$5,958.40
$$

$$
I = 5,958.40 - 800 = 5,158.40
$$

✔ Answer:
- $ A = \$5,958.40 $
- $ I = \$5,158.40 $

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4) Principal = $4,125, Time = 5 years, Rate = 7% compounded annually

- $ P = 4,125 $
- $ r = 0.07 $
- $ t = 5 $

$$
A = 4,125(1 + 0.07)^5 = 4,125(1.07)^5
$$

Calculate $ 1.07^5 $:

- $ 1.07^2 = 1.1449 $
- $ 1.07^4 = (1.1449)^2 ≈ 1.310796 $
- $ 1.07^5 = 1.310796 \times 1.07 ≈ 1.40255 $

$$
A = 4,125 \times 1.40255 ≈ 5,790.32
$$

$$
I = 5,790.32 - 4,125 = 1,665.32
$$

✔ Answer:
- $ A = \$5,790.32 $
- $ I = \$1,665.32 $

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## ✔ Part B: Find the amount payable on $300 after 8 years

a) Compounded annually at 9%

- $ P = 300 $
- $ r = 0.09 $
- $ t = 8 $

$$
A = 300(1 + 0.09)^8 = 300(1.09)^8
$$

Calculate $ 1.09^8 $:

- $ 1.09^2 = 1.1881 $
- $ 1.09^4 = (1.1881)^2 ≈ 1.41158 $
- $ 1.09^8 = (1.41158)^2 ≈ 1.99256 $

$$
A = 300 \times 1.99256 ≈ 597.77
$$

✔ Answer: $597.77

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b) Compounded annually at 35%

- $ P = 300 $
- $ r = 0.35 $
- $ t = 8 $

$$
A = 300(1 + 0.35)^8 = 300(1.35)^8
$$

Calculate $ 1.35^8 $:

We can compute step by step:

- $ 1.35^2 = 1.8225 $
- $ 1.35^4 = (1.8225)^2 ≈ 3.3215 $
- $ 1.35^8 = (3.3215)^2 ≈ 10.998 $

$$
A = 300 \times 10.998 ≈ 3,299.40
$$

✔ Answer: $3,299.40

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## ✔ Final Answers Summary:

Part A:

| Problem | Amount (A) | Interest (I) |
|--------|------------------|-------------------|
| 1 | $13,772.54 | $4,372.54 |
| 2 | $16,452.01 | $3,552.01 |
| 3 | $5,958.40 | $5,158.40 |
| 4 | $5,790.32 | $1,665.32 |

Part B:

a) $597.77
b) $3,299.40

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Let me know if you'd like these calculations shown in a table format or with more steps!