Alice Miller obtains a $100,000 installment loan at an APR of 9% for 36 months. How much could Alice save in finance charges if she had been able to find the loan at an APR of 8% rather than 9%?

To find out how much Alice could save in finance charges by getting an 8% APR loan instead of a 9% APR loan, we can follow these steps:

1. **Step 1: Calculate the monthly payment for the 9% APR loan.**
   The formula to calculate the monthly payment for an installment loan is:

   \[
   M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
   \]
   Where:
   - $M$ is the monthly payment,
   - $P$ is the loan amount (in this case, $100,000),
   - $r$ is the monthly interest rate (APR divided by 12),
   - $n$ is the number of months (36 months here).

   For the 9% APR loan:
   - APR = 9%, so the monthly interest rate $r = \frac{9}{12} \% = 0.0075$.
   - Loan term = 36 months.

   Now we can calculate the monthly payment for this loan.

2. **Step 2: Calculate the monthly payment for the 8% APR loan.**
   For the 8% APR loan:
   - APR = 8%, so the monthly interest rate $r = \frac{8}{12} \% = 0.006667$.
   - Loan term = 36 months.

   Using the same formula, we calculate the monthly payment for the 8% APR loan.

3. **Step 3: Calculate the total finance charges for both loans.**
   The total finance charges for the loan are the difference between the total amount paid and the original loan amount. The total amount paid is simply the monthly payment multiplied by the number of months.

4. **Step 4: Subtract the total finance charges of the 8% APR loan from the 9% APR loan.**
   This gives us the savings in finance charges.

Let me perform these calculations for you.Alice could save approximately **$1,668.12** in finance charges if she had obtained the loan at an 8% APR instead of a 9% APR.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How are finance charges typically calculated on a loan?
2. What impact does loan duration have on total finance charges?
3. How do early repayments affect the finance charges on a loan?
4. What are the advantages of a lower APR besides saving on finance charges?
5. How does the compounding frequency affect the finance charges on loans?

**Tip:** Comparing loans with different APRs over the same term helps identify significant savings, especially for large sums or long durations!

Discover how much Alice could save in finance charges by choosing a loan with an 8% APR instead of 9%. This step-by-step solution covers key finance concepts, including calculating monthly payments and comparing total costs for different APRs. Suitable for Grades 10-12.

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