Calculating Monthly Payment

Oct 13, 2025 by miodeya.com 78 views

Understanding Loan Calculations

When considering a loan, it's essential to understand the various components involved, including the principal amount, interest rate, and loan term. In this scenario, Sofia is considering a 5-year loan for $\$6,000$ at an interest rate of $7\%$ . To make an informed decision, we need to calculate the monthly payment, total interest paid, and the total amount paid over the loan term.

Calculating Monthly Payment

To calculate the monthly payment, we can use the formula:

Monthly Payment = (Principal x Rate x Time) / (1 - (1 + Rate)^(-Time))

Where:

Principal = $\$6,000$
Rate = $7\%$ or $0.07$
Time = 5 years or 60 months

Plugging in the values, we get:

Monthly Payment = ($6,000 x 0.07 x 60) / (1 - (1 + 0.07)^(-60))

Monthly Payment ≈ $123.41

Calculating Total Interest Paid

To calculate the total interest paid, we need to calculate the total amount paid over the loan term and subtract the principal amount.

Total Amount Paid = Monthly Payment x Time

Total Amount Paid ≈ $123.41 x 60

Total Amount Paid ≈ $7,404.60

Total Interest Paid = Total Amount Paid - Principal

Total Interest Paid ≈ $7,404.60 - $6,000

Total Interest Paid ≈ $1,404.60

Calculating Total Amount Paid

To calculate the total amount paid, we need to add the principal amount and the total interest paid.

Total Amount Paid = Principal + Total Interest Paid

Total Amount Paid ≈ $6,000 + $1,404.60

Total Amount Paid ≈ $7,404.60

Loan Amortization Schedule

To understand how the loan is amortized over the loan term, we can create a loan amortization schedule. The schedule will show the monthly payment, interest paid, and principal paid for each month.

Month	Monthly Payment	Interest Paid	Principal Paid
1	$123.41	$43.19	$80.22
2	$123.41	$41.95	$81.46
3	$123.41	$40.72	$82.69
...	...	...	...
60	$123.41	$0.00	$123.41

Conclusion

Understanding Loan Calculations

Calculating Monthly Payment

To calculate the monthly payment, we can use the formula:

Monthly Payment = (Principal x Rate x Time) / (1 - (1 + Rate)^(-Time))

Where:

Principal = $\$6,000$
Rate = $7\%$ or $0.07$
Time = 5 years or 60 months

Plugging in the values, we get:

Monthly Payment = ($6,000 x 0.07 x 60) / (1 - (1 + 0.07)^(-60))

Monthly Payment ≈ $123.41

Calculating Total Interest Paid

To calculate the total interest paid, we need to calculate the total amount paid over the loan term and subtract the principal amount.

Total Amount Paid = Monthly Payment x Time

Total Amount Paid ≈ $123.41 x 60

Total Amount Paid ≈ $7,404.60

Total Interest Paid = Total Amount Paid - Principal

Total Interest Paid ≈ $7,404.60 - $6,000

Total Interest Paid ≈ $1,404.60

Calculating Total Amount Paid

To calculate the total amount paid, we need to add the principal amount and the total interest paid.

Total Amount Paid = Principal + Total Interest Paid

Total Amount Paid ≈ $6,000 + $1,404.60

Total Amount Paid ≈ $7,404.60

Loan Amortization Schedule

To understand how the loan is amortized over the loan term, we can create a loan amortization schedule. The schedule will show the monthly payment, interest paid, and principal paid for each month.

Month	Monthly Payment	Interest Paid	Principal Paid
1	$123.41	$43.19	$80.22
2	$123.41	$41.95	$81.46
3	$123.41	$40.72	$82.69
...	...	...	...
60	$123.41	$0.00	$123.41

Q&A

Q: What is the monthly payment for Sofia's 5-year loan? A: The monthly payment for Sofia's 5-year loan is approximately $123.41.

Q: How much interest will Sofia pay over the 5-year loan term? A: Sofia will pay approximately $1,404.60 in interest over the 5-year loan term.

Q: What is the total amount paid for Sofia's 5-year loan? A: The total amount paid for Sofia's 5-year loan is approximately $7,404.60.

Q: How does the loan amortization schedule work? A: The loan amortization schedule shows the monthly payment, interest paid, and principal paid for each month. The schedule helps to understand how the loan is amortized over the loan term.

Q: Can I change the loan term or interest rate to reduce the monthly payment? A: Yes, you can change the loan term or interest rate to reduce the monthly payment. However, this may also increase the total interest paid over the loan term.

Q: What happens if I miss a monthly payment? A: If you miss a monthly payment, you may be charged a late fee and your credit score may be affected. It's essential to make timely payments to avoid any negative consequences.

Q: Can I prepay the loan to reduce the total interest paid? A: Yes, you can prepay the loan to reduce the total interest paid. However, you should check with the lender to see if there are any prepayment penalties.

Conclusion

In conclusion, Sofia's 5-year loan for $\$6,000$ at an interest rate of $7\%$ will result in a monthly payment of approximately $123.41$ , a total interest paid of approximately $1,404.60$ , and a total amount paid of approximately $7,404.60$ . The loan amortization schedule shows how the loan is amortized over the loan term, with the interest paid decreasing and the principal paid increasing over time.