When you have an add-on loan, the interest on the loan is a percentage of the original amount. Payments are calculated on the loan amount plus the interest (add-on!)

Let’s look at an example.

**Problem 1** Suppose you want to purchase a car for $21,000 with add-on interest at an annual interest rate of 6.2%. If you make monthly payments for 5 years, what will your monthly payment be?

**Solution** Start by calculating the interest you will pay using* I* = *Prt*. Since the amount of the loan is $21,000, *P* = $21,000. Using the rate (*r* = 0.062) and the time (t = 5), we get

*I* = (21000)(0.062)(5) = 6510

This means that we will pay $6510 in interest along with the original $21,000 back to the lender.

Amount paid back = 21,000 + 6510 = 27510

We are going to spread this out over 5 years with monthly payments (total of 60 payments). The amount of each of these payments is

Rounded to the nearest penny.

Now let’s look at how a down payment on a loan affects the payment. A down payment reduces the amount of the loan leading to a lower payment.

**Problem 2** Suppose you want to purchase a car for $21,000 with add-on interest at an annual interest rate of 6.2%. To lower the payments, you make a down payment of $5000. If you make monthly payments for 5 years, what will your monthly payment be?

**Solution** A down payment of $5000 on a $21,000 purchase lowers the amount you borrow to $16,000 (*P* = 16,000). Using the rate (*r* = 0.062) and the time (*t* = 5), we get

*I* = (16000)(0.062)(5) = 4960

This means that we will pay $4960 in interest along with the original $21,000 back to the lender.

Amount paid back = 16,000 + 4960 = 20960

We are going to spread this out over 5 years with monthly payments (total of 60 payments). The amount of each of these payments is

Rounded to the nearest penny. As expected, the payment has gone down compared to Problem 1 above.

Now let’s get real…let’s figure out how much we would need to put down to lower the payment to $400.

**Problem 3** Suppose you want to purchase a car for $21,000 with add-on interest at an annual interest rate of 6.2%. To lower the monthly payment to $300, you need to make a down payment. If you make monthly payments for 5 years, what will your down payment need to be?

**Solution** The key to this problem is to understand what the loan amount needs to be to lower the payment to $400. This means P is our unknown and we want have a monthly payment of $400:

To solve this equation, multiply both sides of the equation by 60:

*P* + *P *(0.062)(5) = 300 × 60

Now let’s do a little simplifying. We can multiply 0.062 × 5 = 0.31 and 400 × 60 = 18000 to give

*P* + 0.31*P* = 18000

1.31*P* = 18000

*P* » 13740.46

The price of the car is $21,000 and the amount to be borrowed is $13740.46, the down payment must be

Down payment = 21000 – 13740.46 = 7259.54

As you might guess, to lower your payment even more requires a bigger down payment.