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Calculate this problem with solution and answer.

To solve this problem, we will use the formula for the simple discount, which is given as:

\[
P = F \times (1 - d \times t)
\]

Where:
- \(P\) is the proceeds (current value, \(P = 50,000\)).
- \(F\) is the face value (future value, \(F = 65,000\)).
- \(d\) is the discount rate (\(d = 13\% = 0.13\)).
- \(t\) is the time in years, which we are trying to find.

Rearranging the formula to solve for \(t\):

\[
t = \frac{1 - \frac{P}{F}}{d}
\]

### Step-by-Step Calculation:

1. **Substitute the values** into the formula:
   \[
   t = \frac{1 - \frac{50,000}{65,000}}{0.13}
   \]

2. **Simplify the fraction**:
   \[
   t = \frac{1 - 0.7692}{0.13}
   \]
   \[
   t = \frac{0.2308}{0.13}
   \]

3. **Divide** to find \(t\):
   \[
   t \approx 1.7754 \text{ years}
   \]

### Final Answer:
The time needed for \( P65,000 \) to be discounted to \( P50,000 \) at a 13% simple discount rate is approximately **1.78 years**.

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Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What happens if the discount rate is increased to 15%?
2. How would the result change if the face value is \( P70,000 \)?
3. What is the effect of changing the proceeds to \( P45,000 \)?
4. How long will it take to discount \( P100,000 \) to \( P85,000 \) at a 10% rate?
5. What is the general formula for simple interest vs. simple discount?

**Tip**: Always check units (e.g., years, months) in time-based financial problems to ensure accuracy.

How long should P65,000 be discounted to have proceeds of P50,000 at a 13% simple discount rate?

Learn how to calculate the time required for P65,000 to be discounted to P50,000 using a 13% simple discount rate. This problem involves simple discount formulas and algebraic manipulation. Suitable for high school students in Grades 10-12.

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