Anna bought a diamond necklace worth ₱185,000. Securing 15% down payment, they agreed to pay 
the remaining for 1 year with 12% annual interest rate.
c. How much is the monthly amortization?

To calculate the monthly amortization for Anna's necklace, we can use the formula for the amortization of a loan. The steps are as follows:

### Given:
- **Cost of the necklace:** ₱185,000
- **Down payment:** 15%
- **Loan duration:** 1 year (12 months)
- **Annual interest rate:** 12%

### Steps:

1. **Calculate the down payment:**
   \[
   \text{Down payment} = 185,000 \times 0.15 = ₱27,750
   \]
   
2. **Remaining amount to be paid (loan amount):**
   \[
   \text{Loan amount} = 185,000 - 27,750 = ₱157,250
   \]

3. **Convert annual interest rate to monthly interest rate:**
   \[
   \text{Monthly interest rate} = \frac{12\%}{12} = 1\% = 0.01
   \]

4. **Number of months (loan term):** 12 months

5. **Amortization formula:**
   \[
   A = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
   \]
   Where:
   - \( A \) = Monthly amortization
   - \( P \) = Loan amount (₱157,250)
   - \( r \) = Monthly interest rate (0.01)
   - \( n \) = Number of months (12)

Now, let's plug in the values and calculate the monthly amortization:

\[
A = 157,250 \times \frac{0.01(1 + 0.01)^{12}}{(1 + 0.01)^{12} - 1}
\]

I'll calculate the result.The monthly amortization for Anna's loan is approximately **₱13,971.47**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What would the total interest paid over the year be?
2. How does the amortization change if the interest rate increases?
3. What if the loan term was extended to 2 years?
4. How much total would Anna pay for the necklace including interest?
5. How does the down payment affect the loan amount?

**Tip:** Making a larger down payment reduces the loan amount and overall interest, lowering monthly payments.

Anna bought a diamond necklace worth ₱185,000. Securing 15% down payment, they agreed to pay the remaining for 1 year with 12% annual interest rate. How much is the monthly amortization?

Learn how to calculate the monthly amortization for a ₱185,000 necklace with a 15% down payment and 12% annual interest rate. The detailed solution involves amortization formulas, interest rate conversion, and algebraic calculations. Suitable for Grades 10-12.

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