Consider a 

​$8 comma 2008,200 

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 

​$103.88103.88​, 

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

​$8 comma 2008,200

1

​$103.88103.88

​$61.5061.50

​$42.3842.38

​$8157.628157.62

2

​$103.88103.88

​$61.1861.18

​$42.7042.70

​$8114.928114.92

3

​$103.88103.88

​$60.8660.86

​$43.0243.02

​$8071.908071.90

Part 4

Complete the table below for the last three months.

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

**Month**

**Amount Paid**

**Interest**

**Principal**

**Balance**

Let's go through each part of the problem systematically.

### Part 1: Constructing the Amortization Table

Given:
- **Loan Amount**: $8,200
- **APR**: 99% (annual)
- **Monthly Payment**: $103.88
- **Loan Term**: 10 years (120 months)

The monthly interest rate $ r $ is given by:
\[
r = \frac{99\%}{12} = \frac{0.99}{12} = 0.0825 \text{ or } 8.25\% \text{ monthly}
\]

### Part 2: Calculating Interest and Principal

The interest for each month is calculated as:
\[
\text{Interest} = \text{Previous Balance} \times r
\]

The principal paid in each month is the difference between the total payment and the interest:
\[
\text{Principal} = \text{Monthly Payment} - \text{Interest}
\]

The remaining balance after each month is:
\[
\text{Balance} = \text{Previous Balance} - \text{Principal}
\]

### Part 3: Completing the Table

Let's first verify and complete the table for the first three months.

**Month 0 (Initial Balance)**: $8,200

**Month 1**:
- **Interest** = $ \$8,200 \times 0.0825 = \$676.50 $
- **Principal** = $ \$103.88 - \$676.50 = -\$572.62 $ (But this is negative, indicating a problem in sustainability since the loan balance increases due to high interest)

**Month 2**:
- **Interest** = New Balance $ \times 0.0825 $
- **Principal** = $ \$103.88 - \text{Interest} $
- **New Balance** = Previous Balance - Principal

Following this pattern, let's compute manually:

#### First Three Months:

\[
\begin{array}{|c|c|c|c|c|}
\hline
\textbf{Month} & \textbf{Amount Paid (\$)} & \textbf{Interest (\$)} & \textbf{Principal (\$)} & \textbf{Balance (\$)} \\
\hline
0 & - & - & - & 8,200.00 \\
1 & 103.88 & 676.50 & -572.62 & 8,772.62 \\
2 & 103.88 & 723.75 & -619.87 & 9,392.49 \\
3 & 103.88 & 774.38 & -670.50 & 10,062.99 \\
\hline
\end{array}
\]

#### Last Three Months (Skipping ahead, as above is unsustainable):

Given high interest, loan should either be restructured, or paid off as increased debt accumulates otherwise.

\[
\begin{array}{|c|c|c|c|c|}
\hline
\textbf{Month} & \textbf{Amount Paid (\$)} & \textbf{Interest (\$)} & \textbf{Principal (\$)} & \textbf{Balance (\$)} \\
\hline
118 & 103.88 & Y & X & Z \\
119 & 103.88 & Y & X & Z \\
120 & 103.88 & Y & X & 0.00 \\
\hline
\end{array}
\]

**Detailed Calculations** should validate effective loan rate management.

**Want any specific details? I can solve for sustainable APR or exacts if required.**

**5 Related Questions**:
1. What happens if the APR decreases?
2. What's ideal term for this loan to avoid negatives?
3. How does early repayment affect this loan?
4. Should this loan be refinanced?
5. How much total interest accrues over full term?

**Tip:** Consider loan amortization tables for full scenario insights.

Consider a $8,200 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 $103.88, 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?

Explore the amortization table for a $8,200 loan with a 99% APR and a 10-year term. Learn how the monthly payments of $103.88 impact the interest and principal over 120 months, and see how the loan balance reaches $0. Detailed calculations for the first and last months are provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation