Sep
22
Are you mystified by how lenders determine your loan payments? Your loan payment is not a magical number conjured out of thin air. In this article we will break down how a loan payment is determined. In this example, we will assume that the loan is set up under simple interest, which means that the interest percentage is compounded monthly. We'll also assume that the loan will begin immediately.
To figure out your loan payments you need to know:
- The loan amount (P)
- The term (or length) of the loan, in months (T)
- The interest rate, expressed as a decimal (I)
To make the calculations cleaner, we'll also say that (J) is the monthly rate of the interest: J = I/12
To figure out our monthly payment (M), the formula looks like this:
M = P x (J/(1 - ( 1 + J) ^ -T)) << Taking 1 + J to the minus-T power, then subtracting this from 1.
For example, let's say that you have taken out a loan of $12,000. You have opted for a loan term of 48 months at 9% interest.
First, assign values to each variable:
Loan amount (P) = 12,000
Term of loan in months (T) = 48
Interest rate as a decimal (I) = .09
Next, we calculate the decimal form of the interest (J) : .09/(12) = .0075 = J
Now we are ready to plug the values into the formula:
M =$12,000 x (.0075/ (1- (1 + .0075) ^-48))
M = $12,000 x (.0075/ (1- (1.0075)^.48))
M = $12,000 x (.0075/(1 - .6986))
M = $12,000 x (.0075/.3014)
M = $12,000 x (.0249)
M = $298.80 per month!
As you can see, the math involved is not all that difficult. If your calculator has a x^y button it is easy to figure out your payment. This is a standard feature of Microsoft's calculator when viewed in Scientific mode. However, if calculating this makes your head hurt, take heart. There is no need to do these calculations yourself. Several websites are available online to calculate the payments for you, using the same formula as described above. Spreadsheet programs such as Excel also have formulas like this one built in, although admittedly this is an advanced feature and requires knowledge of how to use formulas in a spreadsheet.
Why go through this exercise? Simply, this can help you determine whether or not you can afford the car you want. When you plug the numbers into this formula, it quickly becomes apparent whether or not the monthly payments will fit in your budget, saving you from a potentially embarrassing situation at the dealer.