Aug-16-2008
What is the formula for calculating the monthly payment for an Auto Loan?
The bank is financing my wife for 9606.00 at an interest rate of 7.5%. The Term is for 5 yrs (60 months) What should the monthly payments be?
I used to be able to do this, but I think I’m missing something.
Here is how I did my math:
I took $9606.00 and multiplied it times 7.5% and came up with $720.45. Then I added that $720.45 to the $9606.00 and came up with a total of $10,326.45. I then divided the $10,326.45 by 60 (months) and came up with a total of $172.10. Meaning that $172.10 would be my monthly payment.
I went to bankrate.com and used their auto loan calculator and they came up with $192.48
The bank came up with $205.00 (I think they added credit, life, and disability)
So what the HECK am I missing……Please help!
$192.48 is the correct payment.
Using the formula below –
P = principal = 9606.00
I = annual interest rate = 0.075
L = 5 years
Then:
J = monthly interest = 0.075/12 = 0.00625
N = number of months financed = 12 * 5 = 60
Plug all these values into the formula below and you will get the monthly payment. Any insurance, etc. will be added to this amount.
FYI — How you were figuring the amount is incorrect on a couple of points. First, you only calculated interest for 1 year ($720.45) For 5 years, interest would be more like $3600! However, you don’t owe that much interest over the life of the loan, because you keep making payments. Each payment reduces the amount you owe, thus reducing the interest burden on the outstanding principal.
Although the payment amount doesn’t change over the life of the loan, how it gets divided up does. Early on, most of your payment goes to interest, while toward the end of the 5 years, most of your payment applies toward principal.
good luck!
The bankrate.com answer is correct.
9606 = Payment/(.075/12) x (1-1/((1+(.075/12)))^60)
or Payment = 9606*(.075/12)/((1-1/((1+(.075/12)))^60)) = $192.48
You forgot to properly account for the compounding interest and only wanted to pay one year’s worth.
The way you calculated the interest, you only accounted for 1 year of interest (9606 x .075). But after one year you would still owe some of the borrowed money, so the bank will want 7.5% interest on the amount still owed in year 2 (plus the interest on the amounts still owed in years 3, 4, and 5).
The formula is very difficult to write on this website so I’ll break it into two parts.
Let i = the interest rate per period (assume 1 month), so i = 0.075/12 = 0.00625
Let n be the number of periods (months in this case; n=60)
Let a new variable, called “a” be equal to the following-
a = (1-(1+i)^-n) / i = (1-(1.00625)^-60) / 0.00625
a = 49.90530818
The monthly payment then equals $9606 / a = $192.4845342
or simply $192.48.
Note: add the end of 1 month when the first payment is made, $60.04 would be interest owed (9606 x 0.00625) and the remainder of the payment (192.48 – 60.04 = 132.44) would go to reduce the principal amount still owed.) At the end of 2 months when the 2nd payment is made, the outstanding loan balance would be $9606.00 – $132.454 = $9473.56. The interest due on this amount would be $59.21 (9473.56 x 0.00625) and the balance of the 2nd payment would be $133.27 which would go to reduce the principal amount owed.
Bankrate uses a loan amortization table (monthly payment per $1000 to pay principal and interest on installment loan)
9606 / 1000 = 9.606
9.606 x 20.04 (from loan amortization table) = 192.50
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