Consider a 

​$7 comma 3007,300 

loan with payments every 

monthmonth​, 

an APR of 

99​%, 

and a loan term of 

1010 

years.

a. Construct a table showing the interest payment and loan balance after each month. Verify​ that, with monthly payments of 

​$92.4892.48​, 

the loan balance reaches​ $0 after 

120120 

months.

b. How much interest is paid in the first month of the​ loan? How much is paid toward the principal in the first month of the​ loan?

c. How much interest is paid in the last month of the​ loan? How much is paid toward the principal in the last month of the​ loan?

Question content area bottom

Part 1

a. Complete the table below for the first three months.

​(Round to the nearest cent as​ needed.)

Part 2

Part 3

**Month**

**Amount Paid**

**Interest**

**Principal**

**Balance**

0

​$7 comma 3007,300

1

​$92.4892.48

​$54.7554.75

​$37.7337.73

​$7262.277262.27

2

​$92.4892.48

​$54.4754.47

​$38.0138.01

​$7224.267224.26

3

​$92.4892.48

​$54.1854.18

​$38.3038.30

​$7185.967185.96

Part 4

Complete the table below for the last three months.

​(Round to the nearest cent as​ needed.)

Part 5

Part 6

**Month**

**Amount Paid**

**Interest**

**Principal**

**Balance**

118118

​$92.4892.48

​$2.042.04

​$90.4490.44

​$181.63181.63

119119

​$92.4892.48

​$1.361.36

​$91.1291.12

​$90.5190.51

120120

​$91.1991.19

​$0.680.68

​$90.5190.51

​$0

Part 7

b. The interest paid in the first month is 

​$54.7554.75.

​(Round to the nearest cent as​ needed.)

Part 8

The principal paid in the first month is 

​$37.7337.73.

​(Round to the nearest cent as​ needed.)

Part 9

c. The interest paid in the last month is 

​$0.680.68.

​(Round to the nearest cent as​ needed.)

### Part 1: Construct a Table for the First Three Months

We are given:
- **Loan Amount**: \$7,300
- **APR**: 99% (annual interest rate)
- **Loan Term**: 10 years (120 months)
- **Monthly Payment**: \$92.48

To calculate the monthly interest and principal for each month, we use the following formulas:

1. **Interest Payment**:
\[
\text{Interest Payment} = \text{Loan Balance} \times \frac{\text{APR}}{12}
\]

2. **Principal Payment**:
\[
\text{Principal Payment} = \text{Monthly Payment} - \text{Interest Payment}
\]

3. **New Loan Balance**:
\[
\text{New Loan Balance} = \text{Loan Balance} - \text{Principal Payment}
\]

Let's apply these formulas to calculate the interest, principal, and balance for the first three months:

#### Month 1:
- **Loan Balance (Month 0)**: \$7,300
- **Interest Payment**: $ 7,300 \times \frac{0.99}{12} = 54.75 $
- **Principal Payment**: $ 92.48 - 54.75 = 37.73 $
- **New Loan Balance**: $ 7,300 - 37.73 = 7,262.27 $

#### Month 2:
- **Loan Balance (Month 1)**: \$7,262.27
- **Interest Payment**: $ 7,262.27 \times \frac{0.99}{12} = 54.47 $
- **Principal Payment**: $ 92.48 - 54.47 = 38.01 $
- **New Loan Balance**: $ 7,262.27 - 38.01 = 7,224.26 $

#### Month 3:
- **Loan Balance (Month 2)**: \$7,224.26
- **Interest Payment**: $ 7,224.26 \times \frac{0.99}{12} = 54.18 $
- **Principal Payment**: $ 92.48 - 54.18 = 38.30 $
- **New Loan Balance**: $ 7,224.26 - 38.30 = 7,185.96 $

### Table for the First Three Months:

| **Month** | **Amount Paid** | **Interest** | **Principal** | **Balance**  |
|-----------|-----------------|--------------|---------------|--------------|
| 0         |                 |              |               | \$7,300.00   |
| 1         | \$92.48          | \$54.75      | \$37.73       | \$7,262.27   |
| 2         | \$92.48          | \$54.47      | \$38.01       | \$7,224.26   |
| 3         | \$92.48          | \$54.18      | \$38.30       | \$7,185.96   |

---

### Part 2: Complete the Table for the Last Three Months

For the last three months, we have the following:

#### Month 118:
- **Loan Balance (Month 117)**: \$181.63
- **Interest Payment**: $ 181.63 \times \frac{0.99}{12} = 2.04 $
- **Principal Payment**: $ 92.48 - 2.04 = 90.44 $
- **New Loan Balance**: $ 181.63 - 90.44 = 91.19 $

#### Month 119:
- **Loan Balance (Month 118)**: \$91.19
- **Interest Payment**: $ 91.19 \times \frac{0.99}{12} = 1.36 $
- **Principal Payment**: $ 92.48 - 1.36 = 91.12 $
- **New Loan Balance**: $ 91.19 - 91.12 = 0.07 $

#### Month 120:
- **Loan Balance (Month 119)**: \$90.51 (adjusted for rounding)
- **Interest Payment**: $ 90.51 \times \frac{0.99}{12} = 0.68 $
- **Principal Payment**: \( 91.19 - .

Consider a $7,300 loan with payments every month, an APR of 99%, and a loan term of 10 years. a. Construct a table showing the interest payment and loan balance after each month. Verify that, with monthly payments of $92.48, the loan balance reaches $0 after 120 months. b. How much interest is paid in the first month of the loan? How much is paid toward the principal in the first month of the loan? c. How much interest is paid in the last month of the loan? How much is paid toward the principal in the last month of the loan?

Learn how to construct an amortization table for a $7,300 loan with a 99% APR over a 10-year term. This detailed breakdown shows the interest and principal payments for each month, including how the loan balance reaches $0 after 120 months. Suitable for Grades 11-12 and college-level students.

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