Simple Interest Word Problems Worksheet

Let's solve each of these simple interest word problems step by step using the formula:

$$
I = P \cdot r \cdot t
$$

Where:
- $ I $ = Interest earned or paid (in dollars)
- $ P $ = Principal (initial amount, in dollars)
- $ r $ = Annual interest rate (as a decimal)
- $ t $ = Time in years

---

Problem 1

> A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in one year?

Given:
- $ P = 5000 $
- $ r = 2.5\% = 0.025 $
- $ t = 1 $

$$
I = 5000 \cdot 0.025 \cdot 1 = 125
$$

✔ Answer: $125 in interest.

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Problem 2

> Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay? What is the total amount she will repay?

Given:
- $ P = 15,000 $
- $ r = 9\% = 0.09 $
- $ t = 3 $

$$
I = 15,000 \cdot 0.09 \cdot 3 = 4,050
$$

Total repayment = Principal + Interest = $15,000 + $4,050 = $19,050

✔ Answer:
- Interest: $4,050
- Total repayment: $19,050

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Problem 3

> Nancy invested $6000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested?

Given:
- $ I = 450 $
- $ P = 6000 $
- $ r = 3\% = 0.03 $
- $ t = ? $

$$
t = \frac{I}{P \cdot r} = \frac{450}{6000 \cdot 0.03} = \frac{450}{180} = 2.5
$$

✔ Answer: 2.5 years (or 2 years and 6 months)

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Problem 4

> Mr. Johnson borrowed $8000 for 4 years to make home improvements. If he repaid a total of $10,320, at what interest rate did he borrow the money?

Given:
- $ P = 8000 $
- $ t = 4 $
- Total repayment = $10,320 → so interest $ I = 10,320 - 8000 = 2,320 $
- $ r = ? $

$$
r = \frac{I}{P \cdot t} = \frac{2320}{8000 \cdot 4} = \frac{2320}{32,000} = 0.0725 = 7.25\%
$$

✔ Answer: 7.25%

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Problem 5

> John’s parents deposited $1000 into a savings account when he was born. How much will John have after 18 years at a yearly simple interest rate of 3.25%?

Given:
- $ P = 1000 $
- $ r = 3.25\% = 0.0325 $
- $ t = 18 $

$$
I = 1000 \cdot 0.0325 \cdot 18 = 585
$$

Total amount = $1000 + $585 = $1,585

✔ Answer: $1,585

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Problem 6

> Elaine borrowed $2,000 for 3 years at 5% annual simple interest. How much interest will she pay? What is the total amount she will repay?

Given:
- $ P = 2000 $
- $ r = 5\% = 0.05 $
- $ t = 3 $

$$
I = 2000 \cdot 0.05 \cdot 3 = 300
$$

Total repayment = $2000 + $300 = $2,300

✔ Answer:
- Interest: $300
- Total repayment: $2,300

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Problem 7

> TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested?

Given:
- $ I = 200 $
- $ P = 4000 $
- $ r = 2\% = 0.02 $
- $ t = ? $

$$
t = \frac{200}{4000 \cdot 0.02} = \frac{200}{80} = 2.5
$$

✔ Answer: 2.5 years (2 years and 6 months)

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Problem 8

> Mr. Mogi borrowed $9000 for 10 years. He repaid a total of $20,000. At what interest rate did he borrow the money?

Given:
- $ P = 9000 $
- $ t = 10 $
- Total repayment = $20,000 → $ I = 20,000 - 9000 = 11,000 $
- $ r = ? $

$$
r = \frac{11,000}{9000 \cdot 10} = \frac{11,000}{90,000} \approx 0.1222 = 12.22\%
$$

✔ Answer: Approximately 12.22%

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Problem 9

> Bertha deposited $1000 into a retirement account when she was 18. How much will she have after 50 years at a yearly simple interest rate of 7.5%?

Given:
- $ P = 1000 $
- $ r = 7.5\% = 0.075 $
- $ t = 50 $

$$
I = 1000 \cdot 0.075 \cdot 50 = 3,750
$$

Total amount = $1000 + $3,750 = $4,750

✔ Answer: $4,750

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Problem 10

> Joshua borrowed $1000 from his friend and paid back $1050 in six months. What simple annual interest did he pay?

Given:
- $ P = 1000 $
- $ I = 1050 - 1000 = 50 $
- $ t = 6 \text{ months} = 0.5 \text{ years} $
- $ r = ? $

$$
r = \frac{I}{P \cdot t} = \frac{50}{1000 \cdot 0.5} = \frac{50}{500} = 0.10 = 10\%
$$

✔ Answer: 10% annual interest

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $125 |
| 2 | Interest: $4,050; Total: $19,050 |
| 3 | 2.5 years |
| 4 | 7.25% |
| 5 | $1,585 |
| 6 | Interest: $300; Total: $2,300 |
| 7 | 2.5 years |
| 8 | ~12.22% |
| 9 | $4,750 |
| 10 | 10% |

Let me know if you'd like these formatted as a worksheet or explained further!