Sally Seair Buys A Sailboat. The Price, Including Tax, Is $\$5,275.00$. She Finances The Boat Over 36 Months After Making A $\$500$ Down Payment. The True Annual Interest Rate Is $15\%$. What Are Sally's Monthly Payments

Introduction

Sally Seair has finally found her dream sailboat, but she needs to finance it over 36 months. The price of the sailboat, including tax, is $\$5,275.00$. She makes a down payment of $\$500$ and needs to calculate her monthly payments. The true annual interest rate is $15\%$. In this article, we will guide Sally through the process of calculating her monthly payments using the formula for monthly payments on a loan.

Understanding the Formula

The formula for monthly payments on a loan is:

$$M = P \left[ \frac{r(1+r)^n}{(1+r)^n-1} \right]$$

Where:

• $M$ is the monthly payment
• $P$ is the principal loan amount (the amount borrowed)
• $r$ is the monthly interest rate (annual interest rate divided by 12)
• $n$ is the number of payments (the number of months the loan is for)

Calculating the Monthly Interest Rate

The true annual interest rate is $15\%$. To calculate the monthly interest rate, we divide the annual interest rate by 12:

$$r = \frac{0.15}{12} = 0.0125$$

Calculating the Principal Loan Amount

The price of the sailboat, including tax, is $\$5,275.00$. Sally makes a down payment of $\$500$, so the principal loan amount is:

$$P = 5275 - 500 = 4775$$

Calculating the Number of Payments

Sally finances the sailboat over 36 months, so the number of payments is:

$$n = 36$$

Plugging in the Values

Now that we have all the values, we can plug them into the formula:

$$M = 4775 \left[ \frac{0.0125(1+0.0125)^{36}}{(1+0.0125)^{36}-1} \right]$$

Solving for M

Using a calculator or computer program, we can solve for $M$:

$$M = 155.41$$

Conclusion

Sally's monthly payments will be $\$155.41$ for 36 months. This calculation assumes that the interest rate remains constant over the life of the loan and that the monthly payments are made on time. In reality, there may be fees and other charges associated with the loan that are not accounted for in this calculation.

Additional Considerations

When financing a large purchase like a sailboat, it's essential to consider other factors beyond just the monthly payments. These may include:

• Fees: There may be fees associated with the loan, such as origination fees, late payment fees, or prepayment penalties.
• Interest rate: The interest rate may change over the life of the loan, which could affect the monthly payments.
• Loan terms: The loan terms may be negotiable, and Sally may be able to negotiate a better interest rate or longer repayment period.
• Alternative financing options: Sally may be able to explore alternative financing options, such as a personal loan or a credit card, which may have different terms and conditions.

Conclusion

Q&A: Frequently Asked Questions About Calculating Monthly Payments

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

A: The formula for calculating monthly payments on a loan is:

$$M = P \left[ \frac{r(1+r)^n}{(1+r)^n-1} \right]$$

Where:

• $M$ is the monthly payment
• $P$ is the principal loan amount (the amount borrowed)
• $r$ is the monthly interest rate (annual interest rate divided by 12)
• $n$ is the number of payments (the number of months the loan is for)

Q: How do I calculate the monthly interest rate?

A: To calculate the monthly interest rate, you divide the annual interest rate by 12. For example, if the annual interest rate is 15%, the monthly interest rate would be:

$$r = \frac{0.15}{12} = 0.0125$$

Q: What is the principal loan amount?

A: The principal loan amount is the amount borrowed, minus any down payment or other fees. For example, if the price of the sailboat is $5,275 and Sally makes a down payment of $500, the principal loan amount would be:

$$P = 5275 - 500 = 4775$$

Q: How do I calculate the number of payments?

A: The number of payments is the number of months the loan is for. For example, if Sally finances the sailboat over 36 months, the number of payments would be:

$$n = 36$$

Q: What if I have a variable interest rate?

A: If you have a variable interest rate, you will need to calculate the monthly interest rate for each payment period. This can be done using a financial calculator or computer program.

Q: Can I use a financial calculator to calculate my monthly payments?

A: Yes, you can use a financial calculator to calculate your monthly payments. Many financial calculators have a built-in formula for calculating monthly payments on a loan.

Q: What if I make late payments or miss payments?

A: If you make late payments or miss payments, you may be charged fees or penalties. This can increase the total cost of the loan and make it more difficult to pay off the principal amount.

Q: Can I refinance my loan to get a better interest rate?

A: Yes, you can refinance your loan to get a better interest rate. However, this may involve paying fees or penalties, and may also affect your credit score.

Q: What are some other factors I should consider when calculating my monthly payments?

A: Some other factors you should consider when calculating your monthly payments include:

• Fees: There may be fees associated with the loan, such as origination fees, late payment fees, or prepayment penalties.
• Interest rate: The interest rate may change over the life of the loan, which could affect the monthly payments.
• Loan terms: The loan terms may be negotiable, and you may be able to negotiate a better interest rate or longer repayment period.
• Alternative financing options: You may be able to explore alternative financing options, such as a personal loan or a credit card, which may have different terms and conditions.

Conclusion

Calculating monthly payments on a loan requires careful consideration of several factors, including the principal loan amount, monthly interest rate, and number of payments. By using the formula for monthly payments on a loan and considering other factors, you can determine your monthly payments and plan your finances accordingly.