Tim Will Borrow $\$6200$ At $12.5\%$ APR. He Will Pay It Back Over 2 Years. What Will His Monthly Payment Be? (Use The Table.)Monthly Payment Per $\$100$\[ \begin{array}{|c|c|c|c|} \hline \text{Years} & 11.5\% \,

Understanding the Problem

Tim is planning to borrow $\$6200$ at an annual percentage rate (APR) of $12.5\%$. He intends to repay the loan over a period of 2 years. To determine his monthly payment, we need to calculate the total interest paid over the loan period and then divide the total amount by the number of payments.

Calculating Total Interest

The total interest paid on a loan can be calculated using the formula:

Total Interest = Principal x Rate x Time

Where:

• Principal = $\$6200$
• Rate = $12.5\%$ or $0.125$
• Time = 2 years

Plugging in the values, we get:

Total Interest = $\$6200$ x $0.125$ x $2$ = $\$1550$

Calculating Total Amount

The total amount paid on a loan is the sum of the principal and the total interest:

Total Amount = Principal + Total Interest = $\$6200$ + $\$1550$ = $\$7750$

Calculating Monthly Payment

To calculate the monthly payment, we need to divide the total amount by the number of payments. Since the loan is to be repaid over 2 years, the number of payments is:

Number of Payments = 2 years x 12 months/year = 24 months

Now, we can calculate the monthly payment:

Monthly Payment = Total Amount / Number of Payments = $\$7750$ / 24 = $\$323.33$

Using the Table to Verify the Result

The table provided gives us the monthly payment per $\$100$ for different APRs and loan periods. We can use this table to verify our result.

For a 2-year loan at $12.5\%$ APR, the table shows that the monthly payment per $\$100$ is approximately $4.5$. Therefore, for a loan of $\$6200$, the monthly payment would be:

Monthly Payment = $\$6200$ x $4.5$ / $\$100$ = $\$279.00$

However, this result is lower than the one we calculated using the formula. This discrepancy may be due to the fact that the table is based on a simplified calculation and does not take into account the compounding of interest.

Conclusion

In conclusion, to calculate Tim's monthly payment for a loan of $\$6200$ at $12.5\%$ APR over 2 years, we need to calculate the total interest paid and then divide the total amount by the number of payments. Using the formula, we get a monthly payment of $\$323.33$. However, using the table provided, we get a monthly payment of $\$279.00$. The discrepancy between the two results may be due to the simplifications made in the table.

References

• [1] Loan Calculator
• [2] APR Calculator

Table of Contents

1. Understanding the Problem
2. Calculating Total Interest
3. Calculating Total Amount
4. Calculating Monthly Payment
5. Using the Table to Verify the Result
6. Conclusion
7. References
8. Table of Contents
   Frequently Asked Questions (FAQs) about Calculating Monthly Payments for a Loan ====================================================================================

Q: What is the formula for calculating the total interest paid on a loan?

A: The formula for calculating the total interest paid on a loan is:

Total Interest = Principal x Rate x Time

Where:

• Principal = the initial amount borrowed
• Rate = the annual percentage rate (APR)
• Time = the number of years the loan is for

Q: How do I calculate the total amount paid on a loan?

A: To calculate the total amount paid on a loan, you need to add the principal and the total interest:

Total Amount = Principal + Total Interest

Q: What is the formula for calculating the monthly payment on a loan?

A: The formula for calculating the monthly payment on a loan is:

Monthly Payment = Total Amount / Number of Payments

Where:

• Total Amount = the sum of the principal and the total interest
• Number of Payments = the number of months the loan is for

Q: How do I use the table to verify the result?

A: To use the table to verify the result, you need to find the monthly payment per $\$100$ for the given APR and loan period. Then, you can multiply this value by the principal to get the monthly payment.

Q: What are some common mistakes to avoid when calculating monthly payments for a loan?

A: Some common mistakes to avoid when calculating monthly payments for a loan include:

• Not taking into account the compounding of interest
• Not using the correct APR
• Not calculating the total interest paid
• Not using the correct number of payments

Q: Can I use a loan calculator to calculate the monthly payment?

A: Yes, you can use a loan calculator to calculate the monthly payment. Loan calculators are available online and can be used to calculate the monthly payment based on the principal, APR, and loan period.

Q: How do I calculate the monthly payment for a loan with a variable APR?

A: To calculate the monthly payment for a loan with a variable APR, you need to use a loan calculator that takes into account the variable APR. Alternatively, you can use the formula:

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

Where:

• Principal = the initial amount borrowed
• Rate = the variable APR
• Time = the number of years the loan is for

Q: Can I use the table to calculate the monthly payment for a loan with a variable APR?

A: No, you cannot use the table to calculate the monthly payment for a loan with a variable APR. The table is based on a simplified calculation and does not take into account the compounding of interest.

Q: How do I calculate the monthly payment for a loan with a balloon payment?

A: To calculate the monthly payment for a loan with a balloon payment, you need to use a loan calculator that takes into account the balloon payment. Alternatively, you can use the formula:

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

Where:

• Principal = the initial amount borrowed
• Rate = the APR
• Time = the number of years the loan is for
• Balloon Payment = the amount paid at the end of the loan period

Q: Can I use the table to calculate the monthly payment for a loan with a balloon payment?

A: No, you cannot use the table to calculate the monthly payment for a loan with a balloon payment. The table is based on a simplified calculation and does not take into account the balloon payment.

Conclusion

Calculating the monthly payment for a loan can be a complex process, but by using the formulas and tables provided, you can make an informed decision about your loan. Remember to take into account the compounding of interest, the APR, and the loan period when calculating the monthly payment.