A five-year investment had a maturity value of Php 91,000. If the rate was 8% simple interest, what was its present value?

Php 70,000

Php 50,000

Php 65,000

Php 55,000

To find the present value of an investment that matures to Php 91,000 in five years with a simple interest rate of 8%, we can use the formula for calculating the maturity value in simple interest:

\[
A = P (1 + r \times t)
\]

Where:
- \( A \) = maturity value (Php 91,000)
- \( P \) = present value (what we're solving for)
- \( r \) = interest rate (8% or 0.08)
- \( t \) = time in years (5 years)

### Step 1: Substitute the known values into the formula:

\[
91,000 = P (1 + 0.08 \times 5)
\]

\[
91,000 = P (1 + 0.4)
\]

\[
91,000 = P \times 1.4
\]

### Step 2: Solve for \( P \):

\[
P = \frac{91,000}{1.4}
\]

\[
P = 65,000
\]

So, the present value of the investment was **Php 65,000**.

Would you like further details or have any questions? Here are some related questions:

1. How is the simple interest calculated if only maturity and present value are known?
2. How would the present value change if the interest rate were 10%?
3. What is the difference between simple interest and compound interest in calculating present value?
4. How is the maturity value calculated in simple interest investments?
5. How does the time period affect the present value in a simple interest investment?

**Tip:** In simple interest, the principal amount remains constant, and interest does not compound over time.

Calculate the present value of an investment with a maturity value of Php 91,000 after five years at an 8% simple interest rate. This solution covers the concept of simple interest and the formula to determine present value, suitable for Grades 10-12.

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