When you buy a car or a house. your monthly payment is calculated by a method called amort...

When you buy a car or a house. your monthly payment is calculated by a method called amortization. Amortization is the process of paying off a debt by making a given number of equal payments at specified intervals (usually monthly). These payment include the compound interest. With each payment, the amount of interest declines (as the unpaid balance on the loan declines), while the amount paid toward principal increases

If equal payments are made monthly, then the payment amount is calculated according to the following formula:

where t is the number of years to repay the loan.

This monthly payment formula looks pretty formidable, but if we use some variables and do a little algebra, it begins to look a bit better. Let P represent the amount borrowed (the principal) and m represent the monthly interest rate (that is. m = interest rate/ 12). Then your monthly payment is given by

Consider an example. Your rich (and generous) uncle agrees to lend you $3000 at the incredibly low interest rate of 3%, amortized over 2 years. Your monthly interest rate is 0.03/12 = 0.0025, and your monthly payment is

How do you figure out how much of each payment goes to interest and how much to principal? Each month you must calculate the interest on the current loan balance. If the monthly interest rate is 0.0025 and the initial balance is $3000. then the first month’s interest is $7.50. So. or the first payment. only $121 44 is applied toward I he principal, leaving a new balance of $2878.56.

Using the monthly interest rate of 0.0025 on this new balance gives a second month’s interest of $7.20. So,$121.74 is applied toward principal, leaving a new balance of $2756.82.

If you continue on in this manner, you can construct an amortization schedule for your loan. An amortization schedule gives the amount of each payment that goes to interest, the amount that goes to principal, and the new balance after the payment is made. The following table gives the first 4 months of the amortization schedule for this loan.

By the time you finish making payments, bow much interest do you pay on this loan? If you make 24 payments of $128.94, you repay your uncle $3094.56, so you have paid only $94.56 interest on the loan

Now suppose that you have found a great deal on the used car of your dreams-a 4-year-old red Mustang convertible, loaded with options, only one-owner, 44,000 miles-for $ 11 ,50 You really want to buy this car, and you are hoping that you can afford the payment on a$10,000 loan.

Exercise

Of the loans you can afford, which one is the better deal? What is the total price (including tax and interest) that you will pay for the car?