Carlos is taking out a car loan of ₱300,000. The loan offers a 7% annual interest rate. Calculate the total interest Carlos will pay over 5 years if the interest is simple. Then, calculate the total payment if the interest is compounded annually. Advise Carlos on the best option.


The instructions are: 

Task 1: Calculate the total amount using both simple and compound interest for a given

investment or loan after a specified number of years.
Task 2: Analyze and compare which option (simple or compound interest) is more advantageous and provide a recommendation based on financial goals.
Task 3:
Present your findings in a clear and organized report.
Include tables to visually compare the interest growth.
Provide a brief justification for your recommendation.

### Report: Loan Interest Comparison for Carlos

**Loan Amount**: ₱300,000  
**Annual Interest Rate**: 7%  
**Loan Duration**: 5 years

---

### Task 1: Calculation of Total Amount for Simple and Compound Interest

#### 1. **Simple Interest Calculation**

The formula for simple interest is:

\[
I_{\text{simple}} = P \times r \times t
\]

Where:
- \( I_{\text{simple}} \) = Simple interest
- \( P \) = Principal (₱300,000)
- \( r \) = Annual interest rate (7% or 0.07)
- \( t \) = Time (5 years)

**Step 1**: Compute the interest.

\[
I_{\text{simple}} = 300,000 \times 0.07 \times 5 = ₱105,000
\]

**Step 2**: Calculate the total amount to be repaid.

\[
A_{\text{simple}} = P + I_{\text{simple}} = ₱300,000 + ₱105,000 = ₱405,000
\]

Thus, with simple interest, Carlos will repay a total of **₱405,000** after 5 years.

---

#### 2. **Compound Interest Calculation**

The formula for compound interest is:

\[
A_{\text{compound}} = P \times \left(1 + \frac{r}{n}\right)^{n \times t}
\]

Where:
- \( A_{\text{compound}} \) = Total amount with compound interest
- \( P \) = Principal (₱300,000)
- \( r \) = Annual interest rate (7% or 0.07)
- \( n \) = Number of compounding periods per year (1 for annual compounding)
- \( t \) = Time (5 years)

**Step 1**: Compute the total amount with compound interest.

\[
A_{\text{compound}} = 300,000 \times \left(1 + \frac{0.07}{1}\right)^{1 \times 5} 
\]

\[
A_{\text{compound}} = 300,000 \times \left(1.07\right)^5 = 300,000 \times 1.402551
\]

\[
A_{\text{compound}} = ₱420,765.3
\]

Thus, with compound interest, Carlos will repay a total of **₱420,765.30** after 5 years.

---

### Task 2: Comparison of Simple vs. Compound Interest

| **Interest Type** | **Total Amount (₱)** | **Total Interest (₱)** |
|-------------------|----------------------|------------------------|
| Simple Interest    | ₱405,000             | ₱105,000               |
| Compound Interest  | ₱420,765.30          | ₱120,765.30            |

**Key Findings**:
- **Simple Interest** results in Carlos paying a total of ₱405,000, with ₱105,000 as the interest.
- **Compound Interest** results in Carlos paying ₱420,765.30, with ₱120,765.30 as the interest.
- The difference in total repayment between simple and compound interest is ₱15,765.30.

---

### Task 3: Recommendation

From a cost-saving perspective, **simple interest** is more advantageous because Carlos would pay **₱15,765.30 less** than with compound interest. If Carlos's primary goal is to minimize total interest paid, he should opt for a **simple interest** loan.

However, if he values flexibility and wants his payments to align with growing financial commitments, he may consider compound interest, though it will cost more in the long term.

---

### Conclusion

Given that Carlos would save ₱15,765.30 with a simple interest loan over 5 years, the **simple interest option is recommended** to minimize costs. Compound interest would only be favorable if Carlos expects significant increases in his income or financial stability that justify the higher repayment amount.

---

### Follow-up Questions:

1. How would different loan durations (e.g., 3 or 10 years) affect the interest paid?
2. What happens if the loan is compounded semi-annually or monthly instead of annually?
3. What are the risks of taking a compound interest loan if Carlos’s income doesn’t grow?
4. How can Carlos negotiate a lower interest rate with the bank?
5. What would the total payments be if the loan amount were higher or lower?

**Tip**: To lower the total interest paid on a loan, consider making larger or more frequent payments to reduce the principal more quickly.

Carlos is taking out a car loan of ₱300,000. The loan offers a 7% annual interest rate. Calculate the total interest Carlos will pay over 5 years if the interest is simple. Then, calculate the total payment if the interest is compounded annually. Advise Carlos on the best option.

Discover the total amount Carlos will pay for a ₱300,000 car loan at a 7% interest rate over 5 years. Compare simple and compound interest calculations and find out which option is more cost-effective. This detailed guide covers key financial concepts, ideal for Grades 10-12 students.

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