Financing a Purchase

At some point in your life, you are likely to need to borrow money to finance a purchase. For example, most of us will finance the purchase of a car or a home. What is the mathematics behind financing a purchase? When you borrow money from a bank, the bank uses a rather complex equation (or formula) to determine how much you need to pay each month to repay the loan. There are a number of variables that determine the monthly payment. These variables include the amount borrowed, the interest rate, and the length of the loan. The interest rate is based on current economic conditions, the length of the loan, the type of item being purchased, and your credit history.

The following formula gives the monthly payment ? required to pay off a loan amount ? at an annual interest rate ?, expressed as a decimal, but usually given as a percent. The time ?, measured in months, is the length of the loan. For example, a 30-year loan requires 12 X 30=360 monthly payments. Use this formula to complete this project.

1. Interest rates change daily. Many websites post current interest rates on loans. Go to www.bankrate.com and find the current best interest rate on a 60-month new-car purchase loan. Across the top of the of the webpage, choose "Loans" and then "Auto Loans". Change your search to only show 60-month new car loans. Choose the best i.e. lowest interest rate. Sometimes bankrate.com will only show one rate or list the interest rate as 0% which is not interesting and defeats the purpose of the project. If this is the case, I recommend using www.interest.com and choosing 'Cars' and 'Car Loans'. You will have to choose a city and sometimes St. Paul is not listed so choose whichever city is closest to you. Remember, choose the best interest rate for the particular loan you are working with.

a. Use the best rate to determine the monthly payment on a $30,000 automobile loan.

o Round your payment to the nearest cent. Use the formula above and show your work. Do not use an online payment calculator.

o State which lender has the best interest rate and the date you pulled the data.

b. Determine the total amount paid for the loan by multiplying the loan payment by the term of the loan.

o For example, if you calculated your monthly payment to be $350.13 and the term of your loan was 30 months, the total amount you would pay for the loan would be $350.13 per month X 30 months = $10,503.90

c. Determine the total amount of interest paid by subtracting the loan amount paid from part b.

o For example, if the loan amount was $20,000 and your answer from question 2 was $23,000, the total interest paid would be $23,000-$20,000=$3,000.

d. More often than not, we decide how much of a payment we can afford and use that information to determine the loan amount.

i. Suppose you can afford a monthly payment of $500. Use the interest rate from part a to determine the maximum amount you can borrow. In other words, if you know ?, ?, and ?, solve for ?.

ii. If you have $5,000 to put down on the car, how does this change your monthly payment from part i? What will your new monthly payment be? In other words, subtract $5000 from the value of L found in part (i) and recalculate the monthly payment.

2. Repeat question 1a-d using a different new-car purchase loan with a different term than the loan from part a. Keep the principal, $30,000, the same.

o List the term of the loan.

o State the lender, interest rate, and the date you pulled the data.

o Round your answers to the nearest cent.

3. Repeat question 1a-d using a used-car purchase loan with a different term than the loans from problems 1 and 2. Keep the principal, $30,000, the same.

o List the term of the loan.

o State the lender, interest rate, and the date you pulled the data.

o Round your answers to the nearest cent.

4. Based on your calculations from #1-3, which type of loan would you use to purchase a car? Justify your reasoning. Decide on a specific vehicle you would purchase using your chosen loan type. Go to an online automobile website such as www.cars.com, www.edmunds.com, or www.autobytel.com . Use your chosen loan type to determine your monthly payment for your chosen car.