topic Re: How is Auto Interest calculated? in Auto Loans

How is Auto Interest calculated?

Anonymous — Thu, 16 Oct 2014 17:48:58 GMT

This may seem like a very noob question.. But i just need to make sure

i understand this before i go to the dealership tomorrow...

For example sake...

Lets just say your interest rate is 3%

Your monthly payments are $100.

How is the auto loan calculated?

Is it 3% of every single monthly payment you make?

Re: How is Auto Interest calculated?

coterotie — Tue, 21 Oct 2014 01:02:18 GMT

in short, no.

The formula to calculate the payment is as follows:

where

A = payment Amount per period
P = initial Principal (loan amount)
r = interest rate per period
n = total number of payments or periods

So let's say you finance 15,000 for 48 months at 2.5%. Your payment is $328.71. So (15,000 * .025)/360 * 31 = 32.29. So of your first payment 295.71 goes to principal and 32.29 goest to interest leaving you a principal balance of $14,704.29. Next month the calculation is ($14,704.29 *.025)/360 *30 = 30.64. So 298.08 goes to principal and so on for a total of 48 payments. You can download from multiple sites an amortization schedule or use excel. By the way, the 360 is a holdover from an earlier era when these calcs were done by hand. Some banks are using a 365 day year, but many still use 360.

Re: How is Auto Interest calculated?

pipeguy — Tue, 21 Oct 2014 01:03:19 GMT

@coterotie wrote:
in short no.
The formula to calculate the payment is as follows:
where
A = payment Amount per period
P = initial Principal (loan amount)
r = interest rate per period
n = total number of payments or periods
So let's say you finance 15,000 for 48 months at 2.5%. Your payment is $328.71. So (15,000 * .025)/360 * 31 = 32.29. So of your first payment 295.71 goes to principal and 32.29 goest to interest leaving you a principal balance of $14,704.29. Next month the calculation is ($14,704.29 *.025)/360 *30 = 30.64. So 298.08 goes to principal and so on for a total of 48 payments. You can download from multiple sites an amortization schedule or use excel. By the way, the 360 is a holdover from an earlier era when these calcs were done by hand. Some banks are using a 365 day year, but many still use 360.
**********
At least today most every lender uses simple interest (not sure about repo-buy-here-pay-dear lots) rather than the rule of 78's "rule of 78 - sum-of-the-digits method" which was pretty much universal not so long ago. To save you - that don't know - the interest was front loaded on these loans and cost the borrower dearly ANd most had a pre-payment charge if you paid the loan early.
Ahhhh, the good old days....
Edit: Link for those of you that might be interested in the rule of 78 http://www.bankrate.com/brm/news/auto/20010827a.asp

Re: How is Auto Interest calculated?

Anonymous — Tue, 21 Oct 2014 01:04:03 GMT

@coterotie wrote:
in short no.

The formula to calculate the payment is as follows:
where
A = payment Amount per period
P = initial Principal (loan amount)
r = interest rate per period
n = total number of payments or periods
So let's say you finance 15,000 for 48 months at 2.5%. Your payment is $328.71. So (15,000 * .025)/360 * 31 = 32.29. So of your first payment 295.71 goes to principal and 32.29 goest to interest leaving you a principal balance of $14,704.29. Next month the calculation is ($14,704.29 *.025)/360 *30 = 30.64. So 298.08 goes to principal and so on for a total of 48 payments. You can download from multiple sites an amortization schedule or use excel. By the way, the 360 is a holdover from an earlier era when these calcs were done by hand. Some banks are using a 365 day year, but many still use 360.

@mikemsceo wrote:
This may seem like a very noob question.. But i just need to make sure
i understand this before i go to the dealership tomorrow...

For example sake...
Lets just say your interest rate is 3%

Your monthly payments are $100.

How is the auto loan calculated?
Is it 3% of every single monthly payment you make?

Haha.. that is why i asked.. i never learned really how it is calculated. Thanks!

Re: How is Auto Interest calculated?

Hoya08 — Sat, 18 Oct 2014 14:18:38 GMT

Stating a 3% APR is easier to understand than a daily 0.000082191% (365-days) or 0.000083333% (360-days) rate. This is, as a poster stated, because institutions use either 365 or 360 days to calculate interest.

To make interest calculations easy, divide the APR by 12 (number of months) to find the monthly rate (remember to convert % to decimal first)... 0.03/12 = 0.0025

1. Multiply the monthly rate with the loan balance to find the interest charge for that month... 0.0025 x $10,000 = $25.

2. Subtract $25 from $100 to find the amount applied towards the loan balance... $100 - $25 = $75

3. Subtract $75 from the loan balance to figure the new loan balance... $10,000 - $75 = $9,925

Repeat steps 1, 2, and 3. The decrease in monthly interest charge directly equates to increases in principal payments until the loan is paid off.

Re: How is Auto Interest calculated?

Anonymous — Thu, 23 Oct 2014 03:24:51 GMT

@Hoya08 wrote:
Stating a 3% APR is easier to understand than a daily 0.000082191% (365-days) or 0.000083333% (360-days) rate. This is, as a poster stated, because institutions use either 365 or 360 days to calculate interest.

To make interest calculations easy, divide the APR by 12 (number of months) to find the monthly rate (remember to convert % to decimal first)... 0.03/12 = 0.0025

1. Multiply the monthly rate with the loan balance to find the interest charge for that month... 0.0025 x $10,000 = $25.

2. Subtract $25 from $100 to find the amount applied towards the loan balance... $100 - $25 = $75

3. Subtract $75 from the loan balance to figure the new loan balance... $10,000 - $75 = $9,925

Repeat steps 1, 2, and 3. The decrease in monthly interest charge directly equates to increases in principal payments until the loan is paid off.

Thanks for that!!

I guess my next question is....

how is the monthly payment calculated???

Is it...

Car Cost $ 5000

My down Payment: $ 500

Remaining Balance: $ 4500 /36 year term

$125 for 36 months???

Re: How is Auto Interest calculated?

coterotie — Thu, 23 Oct 2014 12:06:29 GMT

Well you could use the formula which would look something like this:

P = 4,500

R= 3%

N = 36

Or you could use the handy dandy calulator available here:

http://www.bankrate.com/calculators/auto/auto-loan-calculator.aspx

Which gives you a payment of 130.87/month for 36 months.

@mikemsceo wrote:
@Hoya08 wrote:
Stating a 3% APR is easier to understand than a daily 0.000082191% (365-days) or 0.000083333% (360-days) rate. This is, as a poster stated, because institutions use either 365 or 360 days to calculate interest.

To make interest calculations easy, divide the APR by 12 (number of months) to find the monthly rate (remember to convert % to decimal first)... 0.03/12 = 0.0025

1. Multiply the monthly rate with the loan balance to find the interest charge for that month... 0.0025 x $10,000 = $25.

2. Subtract $25 from $100 to find the amount applied towards the loan balance... $100 - $25 = $75

3. Subtract $75 from the loan balance to figure the new loan balance... $10,000 - $75 = $9,925

Repeat steps 1, 2, and 3. The decrease in monthly interest charge directly equates to increases in principal payments until the loan is paid off.

Thanks for that!!

I guess my next question is....
how is the monthly payment calculated???

Is it...

Car Cost $ 5000
My down Payment: $ 500

Remaining Balance: $ 4500 /36 year term

$125 for 36 months???

Re: How is Auto Interest calculated?

Hoya08 — Thu, 23 Oct 2014 14:30:13 GMT

Although online calculators are correct, I do my own calcuations.

The formula that's been posted throughout this thread is correct. However, I use Excel (doesn't matter if on a Mac or PC) which handles all the math. Using your example:

Price of: $5000

Down payment of: $500

Loan term of: 36 months

Interest Rate of: 3%

The formula in Excel is =PMT(rate, nper, pv, (fv), (type))

In the simplest terms without getting into technicalities:

PMT is the monthly payment you're tyring to figure

rate is the Interest Rate in decimal form

nper is the Loan Term

pv is the TOTAL loan amount you are requesting

fv is not necessary for this example

type is not necessary for this example

PMT = ?

rate = 0.03/12 (divide by 12 since the interest is compounded monthly - it's daily, but it's easier to work in months and because the loan term is in months)

nper = 36

pv = $4,500 ($5,000 - $500 = $4,500, this is the TOTAL loan you are requesting)

So.... in the Excel cell, you enter

=PMT(0.03/12, 36, $4,500)

The returned number is -130.87 or (130.87) depending on your cell format.

* You will receive a negative number. To avoid minute detail discussions and explanations, don't worry too much about the negative number since it depends on how you utilize or interpret it with other numbers. Just realize that it's the monthly payment (principal and interest).

** This formula is the same to calculate mortgage payments and a sleuth of other financial questions as long as you understand the what you're doing

Re: How is Auto Interest calculated?

Anonymous — Thu, 23 Oct 2014 16:52:07 GMT

Hmmmm

Is it compound interest or simply interest off the principal loan ?

Inactually made a spreadsheet on excel with the formula you gave me

If anybody needs I can upload it ...

Re: How is Auto Interest calculated?

Anonymous — Thu, 23 Oct 2014 17:00:02 GMT

@Hoya08 wrote:
Although online calculators are correct, I do my own calcuations.

The formula that's been posted throughout this thread is correct. However, I use Excel (doesn't matter if on a Mac or PC) which handles all the math. Using your example:

Price of: $5000
Down payment of: $500
Loan term of: 36 months
Interest Rate of: 3%

The formula in Excel is =PMT(rate, nper, pv, (fv), (type))

In the simplest terms without getting into technicalities:

PMT is the monthly payment you're tyring to figure
rate is the Interest Rate in decimal form
nper is the Loan Term
pv is the TOTAL loan amount you are requesting
fv is not necessary for this example
type is not necessary for this example

PMT = ?
rate = 0.03/12 (divide by 12 since the interest is compounded monthly - it's daily, but it's easier to work in months and because the loan term is in months)
nper = 36
pv = $4,500 ($5,000 - $500 = $4,500, this is the TOTAL loan you are requesting)

So.... in the Excel cell, you enter

=PMT(0.03/12, 36, $4,500)

The returned number is -130.87 or (130.87) depending on your cell format.

* You will receive a negative number. To avoid minute detail discussions and explanations, don't worry too much about the negative number since it depends on how you utilize or interpret it with other numbers. Just realize that it's the monthly payment (principal and interest).

** This formula is the same to calculate mortgage payments and a sleuth of other financial questions as long as you understand the what you're doing

Yes!!!! I got something very similar to that! With those exact numbers! Ecxept im using a more realistic 12% for me which is probably what they're going to offer.

I guess paying towards the principal is the best way to cut down interest tremendously withnsuch a high interest rate

Re: How is Auto Interest calculated?

Hoya08 — Thu, 23 Oct 2014 20:09:00 GMT

@mikemsceo wrote:
Hmmmm

Is it compound interest or simply interest off the principal loan ?

Inactually made a spreadsheet on excel with the formula you gave me

If anybody needs I can upload it ...

It's simple interest. I meant to say computed instead of compounded.

Re: How is Auto Interest calculated?

Anonymous — Thu, 23 Oct 2014 22:04:25 GMT

@Hoya08 wrote:
@mikemsceo wrote:
Hmmmm

Is it compound interest or simply interest off the principal loan ?

Inactually made a spreadsheet on excel with the formula you gave me

If anybody needs I can upload it ...
It's simple interest. I meant to say computed instead of compounded.

Since it is simple interest

Every months Payment will be off of the initial Cost of the Car ?

Rather than the new balance...

Is that right?

Re: How is Auto Interest calculated?

StartingOver10 — Fri, 24 Oct 2014 01:02:36 GMT

The payment is the same every month.

It's the allocation of the payment toward the interest and toward the principal.

As you make more payments the principal portion increases and the interest portion decreases.

In any given month the amount you pay over the minimum payment should go toward your principal balance so that the following month there will be less interest due and more paid toward the principal. If you do this every month (make on time payments and pay more than the minimum) you will save a bunch of interest. You can figure out how much interest by going to the link posted upthread earlier at bankrate.com

Re: How is Auto Interest calculated?

Anonymous — Fri, 24 Oct 2014 01:26:36 GMT

Thanks guys been great help..

I went on bankrate and also did the math on my own.. diference is a few bucks..Just arming myself for when i go to the dealer

This one inquiry costed me 20 points

Re: How is Auto Interest calculated?

Hoya08 — Fri, 24 Oct 2014 13:26:02 GMT

It's simple interest as in: the interest charged is the CURRENT balance times the interest rate.

Although the Annual Rate is 3%, the monthly rate is 0.25%. The monthly rate (0.25%) is the significant rate since payments are remitted monthly. In this situation, simple interest is the loan balance times 0.0025. If payments were made Annually, then the significant rate is the Annual Rate (3%). In this situation, simple interest is the loan balance times 0.03.

This is where we start getting into the nuts and bolts of "the time value of money" , which is the basis of the equation presented earlier as well as the Excel formula, and it can get confusing.

If you are interested in the nuts and bolts of "the time value of money", I recommend obtaining an Introduction to Finance book from your local library, or googling for youtube videos and other web resources to help explain it.

To recap how auto loan interest is calculated:

Price: $4,500

APR: 3%

Term: 36 months

The Excel formula is =PMT(0.03/12, 36, $4,500)

The Excel formula returns your monthly payment: $130.87

The monthly payments are fixed and do not change. The monthly payment is a combination of interest and principal payments. As the interest payments decreases each month, the principal payments increases in the excat amount of the interest decrease.

Thie interest payment for the 1st month is the current balance (aka principal) times the monthly interest rate: $4,500 x 0.0025 = $11.25 (simple interest)

The amount applied to the loan balance (the principal) is: $130.87 - $11.25 = $119.62

The new loan balance is $4,500 - $119.62 = $4,380.38

The 2nd months interest charge is the adjusted loan balance times the monthly interest rate: $4,380.38 x 0.0025 = $10.95 (simple interest)

The amount applied to the loan balance is: $130.87 - $10.95 = $119.91

As you can see, the interest payment decreased from $11.25 to $10.95, a $0.30 difference. Since the monthly payment does not change, the $0.30 decrease in interest payments was added to the principal payment. Don't fret over the $0.01 difference as it will be made up in subsequent months due to rounding.

Re: How is Auto Interest calculated?

coterotie — Fri, 24 Oct 2014 12:27:53 GMT

Excel also has an amortization table feature where you can see the portion of principal and interest each month. There are also numerous amortization calculators:

http://www.bankrate.com/calculators/auto/auto-loan-calculator.aspx

Enter your loan data and scroll down to click on the amortization schedule. It will also show you how much you will save by making extra payments over the life of the loan.

And now a plug for savings/investing. If you make the monthly deposits to YOUR savings account. You become the bank and get the BENEFIT of the interest.

Understanding the power of the time value of money is the best lesson anyone can learn.

Now with the power of computers and the internet anyone can do it. Back in the old days, we did all these calcs by hand. When I was taking tests as a Finance undergrad, we couldn't even use calculators. We did all the math by hand and had to be able to do a lot of it in our heads as the tests were all timed.

@Hoya08 wrote:
It's simple interest as in: the interest charged is the CURRENT balance times the interest rate.

Although the Annual Rate is 3%, the monthly rate is 0.25%. The monthly rate (0.25%) is the significant rate since payments are remitted monthly. In this situation, simple interest is the loan balance times 0.0025. If payments were made Annually, then the significant rate is the Annual Rate (3%). In this situation, simple interest is the loan balance times 0.03.

This is where we start getting into the nuts and bolts of "the present value of money" , which is the basis of the equation presented earlier as well as the Excel formula, and it can get confusing.

If you are interested in the nuts and bolts of "the present value of money", I recommend obtaining an Introduction to Finance book from your local library, or googling for youtube videos and other web resources to help explain it.

To recap how auto loan interest is calculated:

Price: $4,500
APR: 3%
Term: 36 months

Your monthly payments are $130.87

The monthly payments are fixed and do not change. The monthly payment is a combination of interest and principal payments. As the interest payments decreases each month, the principal payments increases in the excat amount of the interest decrease.

Thie interest payment for the 1st month is the current balance (aka principal) times the monthly interest rate: $4,500 x 0.0025 = $11.25 (simple interest)

The amount applied to the loan balance (the principal) is: $130.87 - $11.25 = $119.62

The new loan balance is $4,500 - $119.62 = $4,380.38

The 2nd months interest charge is the adjusted loan balance times the monthly interest rate: $4,380.38 x 0.0025 = $10.95 (simple interest)

The amount applied to the loan balance is: $130.87 - $10.95 = $119.91

As you can see, the interest payment decreased from $11.25 to $10.95, a $0.30 difference. Since the monthly payment does not change, the $0.30 decrease in interest payments was added to the principal payment. Don't fret over the $0.01 difference as it will be made up in subsequent months due to rounding.

Re: How is Auto Interest calculated?

Hoya08 — Fri, 24 Oct 2014 13:22:45 GMT

@coterotie wrote:
Excel also has an amortization table feature where you can see the portion of principal and interest each month. There are also numerous amortization calculators:

http://www.bankrate.com/calculators/auto/auto-loan-calculator.aspx

Enter your loan data and scroll down to click on the amortization schedule. It will also show you how much you will save by making extra payments over the life of the loan.

And now a plug for savings/investing. If you make the monthly deposits to YOUR savings account. You become the bank and get the BENEFIT of the interest.

Understanding the power of the time value of money is the best lesson anyone can learn.

Now with the power of computers and the internet anyone can do it. Back in the old days, we did all these calcs by hand. When I was taking tests as a Finance undergrad, we couldn't even use calculators. We did all the math by hand and had to be able to do a lot of it in our heads as the tests were all timed.

I completely agree that everyone should attempt to learn the power of the time value of money. Learning the time value of money has been one of the most beneficial courses I've taken. And thank goodness for spreadsheets and financial calculators!

Re: How is Auto Interest calculated?

Hoya08 — Fri, 24 Oct 2014 13:40:40 GMT

An amortization table can be created to see how much of the monthly payments are applied towards interest charges.

I tend to avoid amortization tables for auto loans. Instead, I use them for tracking mortgage payments.

I assume the question about monthly interest charges on an auto loan is to determine how much interest you will pay over the life of the loan. This is easy to figure out without an amortization table. *[see note below]

Loan: $4,500

APR: 3%

Term: 36 months

With the Excel formula =PMT(0.03/12, 36, $4,500)

The Excel formula returns a $130.87 monthly payment.

Since the payments are fixed for 36 months, your total payment is: monthly payment times term -> $130.87 * 36 = $4,711.16

The difference between the total payments and the original loan balance is the total interest paid: $4,711.16 - $4,500 = $211.16

Keep in mind the $211.16 in interest is the MOST interest you will pay (assuming you do not re-finance). In other words, you're paying about $70 per year in interest, or $6 per month to borrow $4,500.

* [note] Any additional payments to the principal will decrease the total interest paid. However, including additional payments ontop of the monthly payment requires an amortization table or further knowledge of the time value of money to manipulate the Excel formula to determine the total interest paid.

Re: How is Auto Interest calculated?

Anonymous — Fri, 24 Oct 2014 15:18:40 GMT

The posts have helped a lot.

Here is a pic of the calculations I got for a car @ $5000 and an apr of 30% ( I like to calculate the highest possible )

Monthly fpr 36 months at 170 assuming I never pay anything towards the principal. ...

Re: How is Auto Interest calculated?

Hoya08 — Fri, 24 Oct 2014 17:55:39 GMT

Unfortunately, the minimum payment for $5000 @ 30% for 36 months is $212.26. Lenders will not allow you to make less than minimum payments without incurring a fee.

In your scenario of only making $170 instead of $212.26, the loan will be paid off in 54 months.