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Use the following chart to explain how the amount of principal affects the total cost of the loan.

\begin{tabular}{|l|l|l|}
\hline \multicolumn{2}{|c|}{Loan Repayment Period} & \\
\hline & Loan 1 & Loan 2 \\
\hline Principal & \[tex]$5,000 & \$[/tex]6,000 \\
\hline Interest Rate & 6.47\% & 6.47\% \\
\hline Monthly Payment & \[tex]$98 & \$[/tex]117 \\
\hline Loan Repayment Period & 5 years & 5 years \\
\hline Total Cost of the Loan & \[tex]$5,866 & \$[/tex]7,039 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
Certainly! Let's analyze how the principal amount of a loan affects the total cost of the loan using the provided chart.

### Loan 1:

- Principal: [tex]$5,000 - Interest Rate: 6.47% - Monthly Payment: $[/tex]98
- Repayment Period: 5 years
- Total Cost: [tex]$5,866 ### Loan 2: - Principal: $[/tex]6,000
- Interest Rate: 6.47%
- Monthly Payment: [tex]$117 - Repayment Period: 5 years - Total Cost: $[/tex]7,039

### Explanation:

1. Principal Amount:
- Loan 1 starts with a principal amount of [tex]$5,000. - Loan 2 starts with a higher principal amount of $[/tex]6,000.

2. Interest Rate:
- Both loans have the same interest rate of 6.47%.

3. Monthly Payment:
- For Loan 1, the monthly payment is [tex]$98. - For Loan 2, the monthly payment is higher, at $[/tex]117.

4. Repayment Period:
- Both loans have the same repayment period of 5 years, which is 60 months.

5. Total Cost:
- After 5 years of repayment for Loan 1, the total cost amounts to [tex]$5,866. - For Loan 2, the total cost after the same period amounts to $[/tex]7,039.

### Impact of Principal on Total Cost:

- The principal is the initial amount of money borrowed. In both loans, the principal amounts are different while other factors (interest rate and repayment period) are the same.
- Loan 2 has a higher principal ([tex]$6,000) compared to Loan 1 ($[/tex]5,000). Consequently, the monthly payment for Loan 2 is higher ([tex]$117 vs. $[/tex]98).
- Even though the interest rate and the repayment period are identical, the total cost for Loan 2 is higher ([tex]$7,039) compared to Loan 1 ($[/tex]5,866).

### Summary:

The principal amount of a loan significantly impacts the total cost. A higher principal results in higher monthly payments and, ultimately, a higher total cost over the repayment period. This means that even if the interest rate and repayment period are the same, a loan with a larger principal amount will cost more in total due to the higher amount of interest accrued on the larger principal.
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