Activity 1.1

1. If P =P4,500, r = 1.25% and t = 5 years, find the simple interest.

a. What formula will be used?

b. How are you going to express the rate in decimal?

c. How much is the simple interest?

2. If P =P5,000 = 2% and t = 8 mos., find the maturity value.

a. Which formula will you use?

b. How are you going to express the time in years?

c. How much is the maturity value?

Let’s solve each part of Activity 1.1 step by step.

### Problem 1: Simple Interest Calculation
1. **Given Values:**
   - Principal (\( P \)) = ₱4,500
   - Rate (\( r \)) = 1.25%
   - Time (\( t \)) = 5 years

#### Solution:
   a. **Formula for Simple Interest**:
      \[
      \text{Simple Interest (SI)} = P \times r \times t
      \]

   b. **Express the Rate in Decimal**:
      To convert the rate to a decimal, divide by 100:
      \[
      r = \frac{1.25}{100} = 0.0125
      \]

   c. **Calculate the Simple Interest**:
      Substitute the values into the formula:
      \[
      \text{SI} = 4500 \times 0.0125 \times 5
      \]
      \[
      \text{SI} = 281.25
      \]
      So, the simple interest is **₱281.25**.

### Problem 2: Maturity Value Calculation
2. **Given Values:**
   - Principal (\( P \)) = ₱5,000
   - Rate (\( r \)) = 2%
   - Time (\( t \)) = 8 months

#### Solution:
   a. **Formula for Maturity Value**:
      The maturity value (M) includes both the principal and the interest. Thus, we use:
      \[
      M = P + \text{SI} = P \times (1 + r \times t)
      \]

   b. **Express Time in Years**:
      Since 8 months is part of a year, convert it by dividing by 12:
      \[
      t = \frac{8}{12} = \frac{2}{3} \approx 0.6667 \text{ years}
      \]

   c. **Calculate the Maturity Value**:
      First, find the simple interest using the values:
      \[
      \text{SI} = P \times r \times t = 5000 \times 0.02 \times 0.6667
      \]
      \[
      \text{SI} \approx 66.67
      \]
      Now, calculate the maturity value:
      \[
      M = 5000 + 66.67 = 5066.67
      \]
      So, the maturity value is **₱5,066.67**.

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Would you like more details on any step?

### Related Questions
1. What is the difference between simple interest and compound interest?
2. How would the interest change if the rate were compounded annually?
3. How do you calculate time if the interest and rate are given?
4. Why is it essential to convert months to years in these calculations?
5. Can you use the same formula for quarterly or semiannual calculations?

### Tip
Always convert time into years and rate into a decimal format when using the simple interest formula.

Activity 1.1

1. If P =P4,500, r = 1.25% and t = 5 years, find the simple interest.

a. What formula will be used?
b. How are you going to express the rate in decimal?
c. How much is the simple interest?

2. If P =P5,000 = 2% and t = 8 mos., find the maturity value.

a. Which formula will you use?
b. How are you going to express the time in years?
c. How much is the maturity value?

Solve problems involving simple interest and maturity value calculations, using P4,500 at 1.25% for 5 years and P5,000 at 2% for 8 months. Learn to convert interest rates and time, apply formulas, and determine the simple interest and maturity values.

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