Samples of simple interest problem solving

Here are some examples of simple interest problems, along with solutions:

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### 1. **Basic Simple Interest Calculation**

**Problem:**  
If $1000 is invested at a rate of 5% per year for 3 years, what will the simple interest be?

**Solution:**  
The formula for simple interest is:
\[
\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}
\]
Where:
- $ P $ = Principal (initial investment)
- $ R $ = Rate of interest per year
- $ T $ = Time in years

Plugging in the values:
\[
SI = \frac{1000 \times 5 \times 3}{100} = 150
\]

**Answer:** The simple interest earned is $150.

---

### 2. **Finding Total Amount After Interest**

**Problem:**  
How much will $2000 amount to after 4 years at a simple interest rate of 6% per year?

**Solution:**  
First, find the simple interest:
\[
SI = \frac{2000 \times 6 \times 4}{100} = 480
\]

Then, calculate the total amount:
\[
\text{Total Amount (A)} = P + SI = 2000 + 480 = 2480
\]

**Answer:** The total amount after 4 years will be $2480.

---

### 3. **Finding Principal When Simple Interest is Known**

**Problem:**  
An amount earns $250 as simple interest over 5 years at a rate of 5% per year. What was the initial investment (principal)?

**Solution:**  
Using the simple interest formula, rearrange to find $ P $:
\[
P = \frac{SI \times 100}{R \times T}
\]

Plugging in the values:
\[
P = \frac{250 \times 100}{5 \times 5} = 1000
\]

**Answer:** The principal (initial investment) was $1000.

---

### 4. **Finding Interest Rate**

**Problem:**  
A principal of $1200 grows to $1440 in 3 years under simple interest. What was the interest rate?

**Solution:**  
1. Find the simple interest:
   \[
   SI = A - P = 1440 - 1200 = 240
   \]

2. Use the simple interest formula to solve for $ R $:
   \[
   R = \frac{SI \times 100}{P \times T} = \frac{240 \times 100}{1200 \times 3} = 6\%
   \]

**Answer:** The interest rate was 6% per year.

---

### 5. **Finding Time Required to Earn a Specific Interest**

**Problem:**  
How many years will it take for a principal of $500 to earn $150 at a simple interest rate of 10% per year?

**Solution:**  
Rearrange the simple interest formula to find $ T $:
\[
T = \frac{SI \times 100}{P \times R}
\]

Plugging in the values:
\[
T = \frac{150 \times 100}{500 \times 10} = 3
\]

**Answer:** It will take 3 years to earn $150 in interest.

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Would you like more details on any specific example or topic? Here are some questions to expand on this information:

1. How is simple interest different from compound interest?
2. Can you use simple interest formulas in situations with non-annual compounding periods?
3. How would the calculations change if interest were paid monthly instead of yearly?
4. What are the practical applications of simple interest in real-life situations?
5. How do you calculate the time period if the interest rate is provided in months?

**Tip:** Always double-check the units (e.g., years, months) when calculating time in interest problems.

Explore sample problems for solving simple interest with step-by-step solutions. Learn how to calculate interest, total amounts, and principal in real-life scenarios. Suitable for Grades 6-8 students looking to master basic algebra concepts.

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