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To calculate the monthly payment for the installment loan, let’s follow these steps based on the provided data and table:

### Given Information:
- **Amount Financed (P):** $750
- **Annual Percentage Rate (r):** 4.5%
- **Number of Payments per Year (n):** 12
- **Time in Years (t):** 2

### Step 1: Locate the Finance Charge per $100 from the Table
From the table under the **4.5% APR** column and **24 payments** (since $12 \times 2 = 24$), we find the finance charge per $100.

The table value at 4.5% and 24 payments is **$4.75**.

### Step 2: Calculate the Total Finance Charge for $750
The finance charge per $100 is given, so we can scale it up to $750.

1. Convert the amount financed into units of $100:
   \[
   \frac{750}{100} = 7.5
   \]

2. Multiply this by the finance charge per $100:
   \[
   7.5 \times 4.75 = 35.625
   \]

### Step 3: Calculate the Total Repayment Amount
Add the finance charge to the principal amount:
\[
750 + 35.625 = 785.625
\]

### Step 4: Find the Monthly Payment
Since there are 24 payments in total (2 years with 12 payments per year), divide the total amount by 24:
\[
\frac{785.625}{24} = 32.734375
\]

### Step 5: Round to the Nearest Cent
The monthly payment, rounded to the nearest cent, is:
\[
\text{\$32.73}
\]

### Answer:
The monthly payment is **$32.73**.

Would you like further explanation on any part of this process?

---

### Related Questions:
1. How would the payment change if the APR increased to 5.5%?
2. What is the total interest paid over the 2-year period?
3. How would the monthly payment change if the loan term was extended to 3 years?
4. How does the finance charge per $100 change for different APRs?
5. What is the formula used to calculate the finance charge?

### Tip:
When using finance tables, always ensure that the number of payments and APR exactly match your loan details for accurate results.

Determine the monthly payment for an installment loan with an amount financed of $750, an APR of 4.5%, 12 payments per year, and a term of 2 years.

Learn how to determine the monthly payment for an installment loan with an amount financed of $750, APR of 4.5%, and a 2-year term. This solution explains how to use finance charge tables and calculate total repayment, finance charges, and monthly payments. Suitable for Grades 9-12.

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