Suppose you borrow $4500 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end of each month, you make a $250 payment.

Use this information to complete the table below. Round to the nearest cent as needed.



Month

Prior Balance

1.75% Interest
on Prior Balance

Monthly Payment

Ending Balance

1

$4500

2

$4500

$

$250

$

3

$

$

$250

$4154.5

4

$4154.5

$

$250

$

5

$

$69.6

$250

$

We are dealing with a loan repayment schedule where interest is compounded monthly at 1.75%, and a fixed payment of $250 is made each month. Let's fill in the missing values in the table by applying the monthly interest rate and deducting the payment each month.

### Formula for Monthly Interest:
The interest for each month is calculated as:
\[
\text{Interest} = \text{Prior Balance} \times \frac{1.75}{100}
\]
The ending balance is then:
\[
\text{Ending Balance} = \text{Prior Balance} + \text{Interest} - \text{Monthly Payment}
\]

We'll apply this step by step to complete the table.

#### **Month 1:**

1. **Prior Balance** = $4500.00
2. **Interest** = $4500 \times 0.0175 = 78.75$
3. **Monthly Payment** = $250
4. **Ending Balance** = $4500 + 78.75 - 250 = 4328.75$

#### **Month 2:**

1. **Prior Balance** = $4328.75
2. **Interest** = $4328.75 \times 0.0175 = 75.75$
3. **Monthly Payment** = $250
4. **Ending Balance** = $4328.75 + 75.75 - 250 = 4154.50$

#### **Month 3:**

1. **Prior Balance** = $4154.50
2. **Interest** = $4154.50 \times 0.0175 = 72.70$
3. **Monthly Payment** = $250
4. **Ending Balance** = $4154.50 + 72.70 - 250 = 3977.20$

#### **Month 4:**

1. **Prior Balance** = $3977.20
2. **Interest** = $3977.20 \times 0.0175 = 69.60$
3. **Monthly Payment** = $250
4. **Ending Balance** = $3977.20 + 69.60 - 250 = 3796.80$

#### **Month 5:**

1. **Prior Balance** = $3796.80
2. **Interest** = $3796.80 \times 0.0175 = 66.44$
3. **Monthly Payment** = $250
4. **Ending Balance** = $3796.80 + 66.44 - 250 = 3613.24$

### Completed Table:

| Month | Prior Balance | 1.75% Interest on Prior Balance | Monthly Payment | Ending Balance |
|-------|---------------|---------------------------------|-----------------|----------------|
| 1     | $4500.00      | $78.75                          | $250.00         | $4328.75       |
| 2     | $4328.75      | $75.75                          | $250.00         | $4154.50       |
| 3     | $4154.50      | $72.70                          | $250.00         | $3977.20       |
| 4     | $3977.20      | $69.60                          | $250.00         | $3796.80       |
| 5     | $3796.80      | $66.44                          | $250.00         | $3613.24       |

Would you like further details or explanation of any step?

---

### 5 Related Questions:

1. How many months will it take to fully repay the loan?
2. What is the total interest paid over the life of the loan?
3. What if the monthly payment increased to $300—how would that change the schedule?
4. How does the interest rate affect the total cost of the loan?
5. Can you calculate the effective annual interest rate when compounded monthly?

### Tip:
When dealing with loans, always compare the **effective interest rate** to understand the real cost over time.

Suppose you borrow $4500 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end of each month, you make a $250 payment. Use this information to complete the table below. Round to the nearest cent as needed.

This problem helps calculate monthly loan payments with a 21% annual interest rate, compounded monthly at 1.75%. Follow step-by-step to complete a loan repayment table, covering key algebraic and financial concepts. Suitable for Grades 9-12.

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