# Working with Installment Loans

An installment loan is a loan in which the principal and interest are paid back in installments. What makes the installment loan different from a conventional loan or promissory note is that the amount paid in each installment and the number of installments are what drive the interest rate. The interest may or may not be clearly indicated. The annual percentage rate, or APR, is the actual rate of interest charged for the privilege of having the loan. The stated rate and the actual rate are usually completely different things. For example, the stated rate maybe 4%, but if you take into account the effect of monthly compounding, that rate is really 4.07415%. The difference may not seem like much, but it adds up when you’re dealing with lots of money. The formula allows you to determine the annual percentage rate. I introduce this formula in the following section

## Calculating the annual percentage rate

The APR isn’t something that’s widely broadcast on many installment loan contracts; you’ll see the stated interest amount, but the APR takes a little more figuring. It takes into account the effects of compounding and any fees and extra charges. If you’ve ever tried to find a formula for determining APR, you’ve probably discovered that it’s difficult to find one. Most Web sites just want to do the calculations for you. It must be assumed that you really don’t want to tackle a formula or that it’s beyond your capabilities.

### Making purchases using an installment plan

Making purchases with an installment plan allows you to make use of the item or items you’re purchasing while you’re paying for them. Making installment purchases is often a necessary part of doing business. For instance, you may need machinery or supplies to provide services or produce products. The profit from those services or products allows you to make the installment payments. The trick is to be sure that you aren’t paying more than you intended for the machinery or supplies. The stated costs or payments may be deceptive. You may think that you’re getting a good deal — until you do the math and determine that the total payback far exceeds the value of the item.

For example, an advertisement claiming that you can purchase a riding tractor for just \$2,500 down and \$200 each month for the next 5 years may seem like a great deal. But how good a deal is it? Read through the following example to find out.

So, say that you’re deciding whether to purchase a \$10,000 riding tractor using an installment payment plan in which you put down \$2,500 and pay \$200 each month for the next 5 years. What’s the APR on this plan?

You first need to determine the finance charge, because no interest rate is given. The total cost to you is the down payment of \$2,500 plus 5 years of monthly payments of \$200. So your cost is \$2,500 + 5 × 12 × \$200 = \$2,500 + \$12,000 = \$14,500. You’ll end up paying \$14,500 for a riding tractor that costs \$10,000 in cash. So the extra charge is \$14,500 – \$10,000 = \$4,500

Using the formula for APR, the number of payments per year, m, is 12. The principal, P, is \$12,000 (the 5 years of payments), and the total number of payments, n, is 60. By plugging these numbers into the formula, you get

The interest rate comes out to be more than 14.75%.

### Last word

Installment loans are commonly used when making purchases from retailers who are anxious to move their merchandise and earn a profit not only from the markup but also from the interest on the loan. You may be willing to purchase an item using an installment loan if your only option is to let that merchant be your banker. If you aren’t in the position to pay cash or borrow more money from a bank, the installment plan allows you the use of the merchandise immediately