You Purchase A Margarita Truck For $60,000 And Pay $10,000 Down. You Also Agree To Pay The Rest Over The Next 5 Years In Monthly Payments At 8% Percent Interest On The Unpaid Balance. What Will Be The Amount Of Each Payment? Note: Format Is $x,xxx.xx

Understanding the Loan Terms

When purchasing a margarita truck for $60,000, it's essential to understand the loan terms, including the down payment, interest rate, and repayment period. In this scenario, you pay $10,000 down, leaving a balance of $50,000. The remaining amount will be repaid over the next 5 years at an 8% interest rate on the unpaid balance.

Calculating the Monthly Payment

To calculate the monthly payment, we'll use a formula that takes into account the loan amount, interest rate, and repayment period. The formula is:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:

• M = monthly payment
• P = principal loan amount ($50,000)
• i = monthly interest rate (8%/year / 12 months/year = 0.006667)
• n = number of payments (5 years * 12 months/year = 60 months)

Plugging in the values, we get:

M = $50,000 [ 0.006667(1 + 0.006667)^60 ] / [ (1 + 0.006667)^60 – 1] M ≈ $1,043.19

Breaking Down the Monthly Payment

The monthly payment of $1,043.19 includes both interest and principal payments. To understand how much of each, we can break down the payment into its components.

Interest Payment

The interest payment is the amount of interest charged on the outstanding balance for the month. Using the formula for interest payment:

Interest Payment = P * i * (1 + i)^n / [ (1 + i)^n – 1]

Where:

• P = principal loan amount ($50,000)
• i = monthly interest rate (0.006667)
• n = number of payments (60 months)

Plugging in the values, we get:

Interest Payment ≈ $43.19

Principal Payment

The principal payment is the amount of the monthly payment that goes towards reducing the outstanding balance. To calculate the principal payment, we subtract the interest payment from the monthly payment:

Principal Payment = Monthly Payment – Interest Payment = $1,043.19 – $43.19 ≈ $1,000.00

Repayment Schedule

To visualize the repayment schedule, we can create a table showing the outstanding balance, interest payment, principal payment, and total payment for each month.

Month	Outstanding Balance	Interest Payment	Principal Payment	Total Payment
1	$50,000.00	$43.19	$1,000.00	$1,043.19
2	$49,000.00	$42.83	$1,000.00	$1,042.83
3	$48,000.00	$42.47	$1,000.00	$1,042.47
...	...	...	...	...
60	$0.00	$0.00	$1,043.19	$1,043.19

Conclusion

Q: What is the total interest paid over the 5-year period?

A: To calculate the total interest paid, we can use the formula:

Total Interest = P * i * n

Where:

• P = principal loan amount ($50,000)
• i = annual interest rate (8%)
• n = number of years (5)

Plugging in the values, we get:

Total Interest ≈ $50,000 * 0.08 * 5 ≈ $20,000.00

So, the total interest paid over the 5-year period is approximately $20,000.00.

Q: How much of the total payment goes towards interest in the first year?

A: To calculate the interest paid in the first year, we can use the formula:

Interest Paid in First Year = P * i

Where:

• P = principal loan amount ($50,000)
• i = annual interest rate (8%)

Plugging in the values, we get:

Interest Paid in First Year ≈ $50,000 * 0.08 ≈ $4,000.00

So, approximately $4,000.00 of the total payment goes towards interest in the first year.

Q: How much of the total payment goes towards principal in the first year?

A: To calculate the principal paid in the first year, we can subtract the interest paid in the first year from the total payment:

Principal Paid in First Year = Total Payment – Interest Paid in First Year = $1,043.19 * 12 – $4,000.00 ≈ $11,208.28

So, approximately $11,208.28 of the total payment goes towards principal in the first year.

Q: What is the total amount paid over the 5-year period?

A: To calculate the total amount paid, we can multiply the monthly payment by the number of payments:

Total Amount Paid = Monthly Payment * Number of Payments = $1,043.19 * 60 ≈ $62,439.40

So, the total amount paid over the 5-year period is approximately $62,439.40.

Q: How much of the total amount paid goes towards interest?

A: To calculate the total interest paid, we can subtract the principal paid from the total amount paid:

Total Interest Paid = Total Amount Paid – Principal Paid = $62,439.40 – $50,000.00 ≈ $12,439.40

So, approximately $12,439.40 of the total amount paid goes towards interest.

Q: What is the effective interest rate of the loan?

A: To calculate the effective interest rate, we can use the formula:

Effective Interest Rate = (Total Interest Paid / Principal Paid) * 100

Where:

• Total Interest Paid = $12,439.40
• Principal Paid = $50,000.00

Plugging in the values, we get:

Effective Interest Rate ≈ (12,439.40 / 50,000.00) * 100 ≈ 24.79%

So, the effective interest rate of the loan is approximately 24.79%.

Q: Can I prepay the loan without penalty?

A: Yes, you can prepay the loan without penalty. However, you should check the loan agreement to confirm that there are no prepayment penalties.

Q: Can I make extra payments towards the principal?

A: Yes, you can make extra payments towards the principal. This can help reduce the outstanding balance and save on interest payments.

Q: Can I refinance the loan if interest rates drop?

A: Yes, you can refinance the loan if interest rates drop. However, you should check the loan agreement to confirm that there are no prepayment penalties and that refinancing is allowed.