Mr. J Reyes borrowed money from the bank. He received from the bank P1,842 and promised to pay P2,000 at the end of 10 months.
Determine the rate of simple interest.

To determine the rate of simple interest, we can use the simple interest formula:

\[
A = P(1 + rt)
\]

Where:
- \( A \) is the amount to be paid back (P2,000).
- \( P \) is the principal, or the amount borrowed (P1,842).
- \( r \) is the rate of interest (what we need to find).
- \( t \) is the time period in years (10 months = \( \frac{10}{12} \) years).

### Step-by-step solution:

1. **Write the formula:**

\[
A = P(1 + rt)
\]

2. **Substitute the known values:**

\[
2,000 = 1,842(1 + r \times \frac{10}{12})
\]

3. **Simplify the equation:**

\[
2,000 = 1,842\left(1 + \frac{5r}{6}\right)
\]

4. **Isolate the term involving \( r \):**

\[
\frac{2,000}{1,842} = 1 + \frac{5r}{6}
\]

5. **Simplify the fraction:**

\[
1.0857 \approx 1 + \frac{5r}{6}
\]

6. **Subtract 1 from both sides:**

\[
0.0857 \approx \frac{5r}{6}
\]

7. **Solve for \( r \):**

\[
r = \frac{0.0857 \times 6}{5} \approx 0.1028
\]

8. **Convert to percentage:**

\[
r \approx 10.28\%
\]

### Final Answer:
The rate of simple interest is approximately **10.28%**.

Would you like any more details or have any questions?

Here are 5 related questions to consider:
1. What would the interest amount be if the loan were for 5 months instead of 10?
2. How much interest would be paid if the loan was extended to 1 year at the same rate?
3. How would the rate change if Mr. Reyes borrowed P1,000 instead of P1,842?
4. What is the total interest paid on the loan in pesos?
5. How would the time to repay affect the total amount to be paid?

**Tip:** Simple interest is directly proportional to both time and the principal amount, so even slight changes in either will affect the final amount significantly.

Mr. J Reyes borrowed money from the bank. He received from the bank P1,842 and promised to pay P2,000 at the end of 10 months. Determine the rate of simple interest.

Discover how to calculate the simple interest rate for a loan of P1,842 to be repaid as P2,000 over 10 months. This problem involves applying the simple interest formula and converting the interest rate to a percentage. Ideal for students in Grades 9-10.

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