examples of problem solving finding the maturity value in simple interest

To find the maturity value in simple interest, you can use the formula:

\[ 
\text{Maturity Value} = P + I 
\]

Where:
- $ P $ is the principal amount (the initial amount of money).
- $ I $ is the interest earned, calculated as:

\[ 
I = P \times r \times t 
\]

Here:
- $ r $ is the rate of interest (as a decimal).
- $ t $ is the time the money is invested or borrowed (in years).

### Examples

1. **Example 1:**
   - Principal (P): $1,000
   - Rate (r): 5% (0.05 as a decimal)
   - Time (t): 3 years

   **Calculating Interest:**
   \[
   I = 1000 \times 0.05 \times 3 = 150
   \]

   **Maturity Value:**
   \[
   \text{Maturity Value} = 1000 + 150 = 1150
   \]

2. **Example 2:**
   - Principal (P): $500
   - Rate (r): 4% (0.04)
   - Time (t): 2 years

   **Calculating Interest:**
   \[
   I = 500 \times 0.04 \times 2 = 40
   \]

   **Maturity Value:**
   \[
   \text{Maturity Value} = 500 + 40 = 540
   \]

3. **Example 3:**
   - Principal (P): $2,000
   - Rate (r): 6% (0.06)
   - Time (t): 5 years

   **Calculating Interest:**
   \[
   I = 2000 \times 0.06 \times 5 = 600
   \]

   **Maturity Value:**
   \[
   \text{Maturity Value} = 2000 + 600 = 2600
   \]

4. **Example 4:**
   - Principal (P): $750
   - Rate (r): 3% (0.03)
   - Time (t): 4 years

   **Calculating Interest:**
   \[
   I = 750 \times 0.03 \times 4 = 90
   \]

   **Maturity Value:**
   \[
   \text{Maturity Value} = 750 + 90 = 840
   \]

5. **Example 5:**
   - Principal (P): $1,500
   - Rate (r): 7% (0.07)
   - Time (t): 1 year

   **Calculating Interest:**
   \[
   I = 1500 \times 0.07 \times 1 = 105
   \]

   **Maturity Value:**
   \[
   \text{Maturity Value} = 1500 + 105 = 1605
   \]

### Summary
To calculate the maturity value, find the interest using the principal, rate, and time, and then add it to the principal.

Would you like further details on any of these examples or any specific questions? Here are some follow-up questions:

1. What happens if the interest rate is compounded instead of being simple?
2. How would the maturity value change if the principal amount is increased?
3. Can you explain how to convert a percentage rate to a decimal?
4. What if the time period is given in months instead of years?
5. How does inflation affect the maturity value over time?

**Tip:** Always ensure to convert the interest rate into a decimal when using it in calculations.

Explore how to calculate maturity value using simple interest with detailed examples. Learn the formulas and see practical applications for different principal amounts, interest rates, and time periods, suitable for students in Grades 9-12.

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