Mr. Santos borrowed 35, 400 pesos on June 1, 2021 and paid on December 1, 2021 with an interest of 5% compounded semiannually. How much did he pay then?

To calculate how much Mr. Santos paid on December 1, 2021, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \( A \) is the amount to be paid
- \( P \) is the principal amount (35,400 pesos)
- \( r \) is the annual interest rate (5% or 0.05)
- \( n \) is the number of times the interest is compounded per year (semiannually means \( n = 2 \))
- \( t \) is the time the money is invested or borrowed for, in years

### Step 1: Identify the variables
- \( P = 35,400 \, \text{pesos} \)
- \( r = 0.05 \)
- \( n = 2 \)
- \( t = \frac{6 \, \text{months}}{12 \, \text{months/year}} = 0.5 \, \text{years} \)

### Step 2: Plug the values into the formula
\[
A = 35,400 \left(1 + \frac{0.05}{2}\right)^{2 \times 0.5}
\]

\[
A = 35,400 \left(1 + 0.025\right)^1
\]

\[
A = 35,400 \times 1.025
\]

\[
A = 36,285 \, \text{pesos}
\]

### Conclusion:
Mr. Santos paid **36,285 pesos** on December 1, 2021.

Would you like to know more details or have any questions?

Here are some related questions you might find interesting:
1. How would the amount change if the interest were compounded quarterly?
2. What would be the total amount paid if the interest rate were 7% instead of 5%?
3. How much would the payment be if the loan period were 1 year instead of 6 months?
4. What is the difference between simple interest and compound interest in this context?
5. How would the calculation change if the interest were compounded annually instead of semiannually?

**Tip:** Always double-check the time period used when calculating compound interest, especially when dealing with different compounding frequencies.

Learn how to calculate compound interest with semiannual compounding using Mr. Santos' example. Understand the formula A = P * (1 + r/n)^(nt) with detailed steps and calculations. Suitable for high school students and anyone interested in financial mathematics.

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