Amy has a master's degree in secondary education and has taught math at a public charter high school.
Watch this video lesson and learn how you can calculate your monthly payment when you are thinking of purchasing a car. Okay, you can also use this formula whenever you are getting a loan!
So, I saw my dream car on the road yesterday. I went to the dealer today to see about buying it. The car dealer tells me that he has this great deal on the car that I want. Apparently, only for today, he is selling the car for $45,000 with an annual percentage rate of 7.5%. I would only be making monthly payments for five years, he says. He says he did some calculations and this is the best deal he has. Will I take it? My job only pays me so much per month. Can I afford it? If you were in my shoes, what would you do? Would you just go ahead and buy it and hope for the best? Is there a better method? One that won't potentially leave me broke? And besides, how much do I need to pay each month? Since we are talking math here, there definitely is a better way to figure all this out than just signing the agreement and hoping for the best.
And what is this better way? If you haven't already guessed, it's with a formula! Our world runs on formulas, after all. The formula that we will use to help us out is called the loan payment amount formula. It is this:
M is the monthly payment, P is the loan amount, J is the monthly interest and N the total number of payments.
Does this look complicated? Don't worry, it's not so bad once you start working with it. It just looks bad right now because of all the letters. Once we put numbers in place of the letters, you will see that it gets much better!
Monthly Interest and Number of Payments
Before you start plugging in numbers, let me explain how to figure out the numbers for J and N. These two numbers are not as straightforward as the number P, which is simply your loan amount (in our case $45,000). You see, J stands for the monthly interest, but we are only given the annual interest rate, our annual percentage rate. The same with N, our total number of payments; we are told that we are going to be making monthly payments for five years. That doesn't tell us the total number of payments we will make, so we need to calculate this, too.
To calculate J, we take our annual percentage rate and we divide it by 100 times the number of payments we are making per year. Since we are making monthly payments, the number of payments per year is 12. So, our J is our annual percentage rate divided by 100 * 12 = 1200. Our annual percentage rate is 7.5%, so our J is 7.5 / 1200 = 0.00625.
Our N is the total number of payments we need to make. If we make 12 payments per year for 5 years, our total number of payments will be 12 * 5 = 60. So, our N is 60. Now that we have both J and N, we can go finish our calculation.
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We are trying to find M, our monthly payment amount, so we leave M as it is. The P is the loan amount, which is $45,000. So, I can plug that number into our formula. I can also plug in 0.00625 for J, which we calculated, along with 60 for N. Doing this I get M = (45,000 * 0.00625) / (1 - (1 + 0.00625)^-60).
Hey, this doesn't look so bad now. All I have are numbers, and I certainly know what to do with these. Let's get cracking at this now. First, we will add what is inside the parentheses to get 1 + 0.00625 = 1.00625. Then we take this number and take it to our power of -60 to get 1.00625^-60 = 0.688. Now we can multiply the top to get 45,000 * 0.00625 = 281.25, and we can finish evaluating the denominator by subtracting 1 - 0.688 to get 0.312. Now we divide 281.25 by 0.312 to get our monthly payment of $901.44.
Hmm, now that I know that I would have to pay $901.44 every single month for five years, I'm going to pass on my dream car. I'll settle for a model of it instead. After all, I did see a little toy model of my dream car that only costs $30 at the toy store the other day.
Now you know what to do if you ever are in this kind of situation. See if you can remember. We started with our loan payment amount formula, which is this:
M is the monthly payment, P is the loan amount, J is the monthly interest and N is the total number of payments. To calculate J, our monthly interest, we take our annual percentage rate and divide it by 100 times the number of payments we will be making per year. To calculate N, we multiply the number of payments per year by the number of years we will be making those payments. Once we have all our numbers, we plug them in and evaluate away.
Following this lesson, you'll be able to:
Recall the loan payment amount formula and define its variables
Calculate how much a monthly loan payment would be using this formula
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