Printable primary math worksheet for math grades 1 to 6 based on ... - Free Printable

Problem Set: Simple Interest Problems

We will solve each problem step by step using the formula for simple interest:
\[
\text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100}
\]
The total amount after interest is calculated as:
\[
\text{Total Amount} = \text{Principal} + \text{Simple Interest}
\]

---

#### Problem 1:
Danny kept 100,000 Yen in a saving account at a simple interest rate of 11% per year. How much interest will he get after 10 years?

- Given:
- Principal (\( P \)) = 100,000 Yen
- Rate (\( R \)) = 11% per year
- Time (\( T \)) = 10 years

- Formula for Simple Interest:
\[
\text{SI} = \frac{P \times R \times T}{100}
\]

- Substitute the values:
\[
\text{SI} = \frac{100,000 \times 11 \times 10}{100}
\]

- Simplify:
\[
\text{SI} = \frac{100,000 \times 110}{100} = \frac{11,000,000}{100} = 110,000 \text{ Yen}
\]

- Answer:
\[
\boxed{110,000 \text{ Yen}}
\]

---

#### Problem 2:
Ferry lent 1,000 dollars to a friend for 2 years at a simple interest rate of 7% p.a. How much was repaid after 2 years?

- Given:
- Principal (\( P \)) = 1,000 dollars
- Rate (\( R \)) = 7% per year
- Time (\( T \)) = 2 years

- Formula for Simple Interest:
\[
\text{SI} = \frac{P \times R \times T}{100}
\]

- Substitute the values:
\[
\text{SI} = \frac{1,000 \times 7 \times 2}{100}
\]

- Simplify:
\[
\text{SI} = \frac{1,000 \times 14}{100} = \frac{14,000}{100} = 140 \text{ dollars}
\]

- Total Repayment:
\[
\text{Total Repayment} = \text{Principal} + \text{Simple Interest} = 1,000 + 140 = 1,140 \text{ dollars}
\]

- Answer:
\[
\boxed{1,140 \text{ dollars}}
\]

---

#### Problem 3:
Jacky put 9,000 dollars in an account that pays her a yearly 3% simple interest. What will be the total balance of her account after 7 years?

- Given:
- Principal (\( P \)) = 9,000 dollars
- Rate (\( R \)) = 3% per year
- Time (\( T \)) = 7 years

- Formula for Simple Interest:
\[
\text{SI} = \frac{P \times R \times T}{100}
\]

- Substitute the values:
\[
\text{SI} = \frac{9,000 \times 3 \times 7}{100}
\]

- Simplify:
\[
\text{SI} = \frac{9,000 \times 21}{100} = \frac{189,000}{100} = 1,890 \text{ dollars}
\]

- Total Balance:
\[
\text{Total Balance} = \text{Principal} + \text{Simple Interest} = 9,000 + 1,890 = 10,890 \text{ dollars}
\]

- Answer:
\[
\boxed{10,890 \text{ dollars}}
\]

---

#### Problem 4:
John paid $2,300 to repay a loan given to him at a 3% simple interest rate for 5 years. How much money did he borrow initially?

- Given:
- Total Repayment = 2,300 dollars
- Rate (\( R \)) = 3% per year
- Time (\( T \)) = 5 years

- Let the Principal be \( P \).
- Formula for Simple Interest:
\[
\text{SI} = \frac{P \times R \times T}{100}
\]

- Total Repayment is the sum of Principal and Interest:
\[
\text{Total Repayment} = P + \text{SI}
\]
\[
2,300 = P + \frac{P \times 3 \times 5}{100}
\]

- Simplify the Interest term:
\[
2,300 = P + \frac{15P}{100}
\]
\[
2,300 = P + 0.15P
\]
\[
2,300 = 1.15P
\]

- Solve for \( P \):
\[
P = \frac{2,300}{1.15} = 2,000 \text{ dollars}
\]

- Answer:
\[
\boxed{2,000 \text{ dollars}}
\]

---

#### Problem 5:
If you put $2,000 in an account at an annual simple interest rate of 5%, how long will it take your balance to grow to $2,600?

- Given:
- Principal (\( P \)) = 2,000 dollars
- Rate (\( R \)) = 5% per year
- Total Amount = 2,600 dollars

- Formula for Total Amount:
\[
\text{Total Amount} = P + \text{SI}
\]
\[
2,600 = 2,000 + \text{SI}
\]

- Solve for Simple Interest:
\[
\text{SI} = 2,600 - 2,000 = 600 \text{ dollars}
\]

- Formula for Simple Interest:
\[
\text{SI} = \frac{P \times R \times T}{100}
\]

- Substitute the values:
\[
600 = \frac{2,000 \times 5 \times T}{100}
\]

- Simplify:
\[
600 = \frac{10,000T}{100}
\]
\[
600 = 100T
\]
\[
T = \frac{600}{100} = 6 \text{ years}
\]

- Answer:
\[
\boxed{6 \text{ years}}
\]

---

#### Problem 6:
Jenny deposited $3,000 in her account. After 4 years, her account balance was $4,800. What was the simple interest rate of her account?

- Given:
- Principal (\( P \)) = 3,000 dollars
- Total Amount = 4,800 dollars
- Time (\( T \)) = 4 years

- Formula for Total Amount:
\[
\text{Total Amount} = P + \text{SI}
\]
\[
4,800 = 3,000 + \text{SI}
\]

- Solve for Simple Interest:
\[
\text{SI} = 4,800 - 3,000 = 1,800 \text{ dollars}
\]

- Formula for Simple Interest:
\[
\text{SI} = \frac{P \times R \times T}{100}
\]

- Substitute the values:
\[
1,800 = \frac{3,000 \times R \times 4}{100}
\]

- Simplify:
\[
1,800 = \frac{12,000R}{100}
\]
\[
1,800 = 120R
\]
\[
R = \frac{1,800}{120} = 15 \text{ %}
\]

- Answer:
\[
\boxed{15 \text{ %}}
\]

---

Final Answers:

1. \(\boxed{110,000 \text{ Yen}}\)
2. \(\boxed{1,140 \text{ dollars}}\)
3. \(\boxed{10,890 \text{ dollars}}\)
4. \(\boxed{2,000 \text{ dollars}}\)
5. \(\boxed{6 \text{ years}}\)
6. \(\boxed{15 \text{ %}}\)