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how is automobile financing interest calculated?

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skim milk

Diamond Member
Total Finance Amount: $23,606.00

It was at 2.9% for 60 months

I have made 7 payments already.

how are the monthly interest figures calculated? It ranges from 44 to 78 per month on top of the principal amount

I called but their office is closed for the week

is the interest amount below correct? if financed at 2.9%

Principal Interest Misc Total
10/27/2008 Monthly Payment $370.07 $53.56 $0.00 $423.63
9/27/2008 Monthly Payment $345.68 $77.95 $0.00 $423.63
8/15/2008 Monthly Payment $379.40 $44.23 $0.00 $423.63
7/22/2008 Monthly Payment $348.82 $74.81 $0.00 $423.63
 
Usually your payments go towards interest first, then the principal. Call them make a 10K payment towards PRINCIPAL and see that amount drops.
 
Originally posted by: skim milk
Total Finance Amount: $23,606.00

It was at 2.9% for 60 months

I have made 7 payments already.

how are the monthly interest figures calculated? It ranges from 44 to 78 per month on top of the principal amount

I called but their office is closed for the week

is the interest amount below correct? if financed at 2.9%

Principal Interest Misc Total
10/27/2008 Monthly Payment $370.07 $53.56 $0.00 $423.63
9/27/2008 Monthly Payment $345.68 $77.95 $0.00 $423.63
8/15/2008 Monthly Payment $379.40 $44.23 $0.00 $423.63
7/22/2008 Monthly Payment $348.82 $74.81 $0.00 $423.63
Click to expand...

365 days in a year, 12 months per year = ~30.4 days per month
Assuming you make a payment every 30.4 days, your first 7 interest payments would be:
$57.05
$56.16
$55.28
$54.39
$53.50
$52.60
$51.71

However, you have not been making payments every 30.4 days. From 7/22/08 to 8/15/08 24 days passed. Since you paid before the 30.4 days, there was less interest accrued between July and August.

From August to September 43 days passed between payments. Since you were at more than 30.4 days, you accrued extra interest.

From September to October, about 30 days passed so you were assessed the correct interest.

Basically, since your payments haven't been at regular intervals, your interest charges aren't regular either.
 
Originally posted by: sactoking


365 days in a year, 12 months per year = ~30.4 days per month
Assuming you make a payment every 30.4 days, your first 7 interest payments would be:
$57.05
$56.16
$55.28
$54.39
$53.50
$52.60
$51.71

However, you have not been making payments every 30.4 days. From 7/22/08 to 8/15/08 24 days passed. Since you paid before the 30.4 days, there was less interest accrued between July and August.

From August to September 43 days passed between payments. Since you were at more than 30.4 days, you accrued extra interest.

From September to October, about 30 days passed so you were assessed the correct interest.

Basically, since your payments haven't been at regular intervals, your interest charges aren't regular either.
Click to expand...

can you show me the math formula used to come up with those numbers?
 
Sure, it's not too hard.

Here's what I know:
Initial Loan Balance- $23,606
Interest Rate- 2.9%
Term of the loan- 60 months

Using those three items, I can solve for your monthly payment using the present value of an annuity equation. The equation is:

PVA = PMT[1-1/(1+i)^n]

Where:

PVA is 'Present Value of the Annuity'
PMT is 'Payment'
i is 'interest per term'
n is 'number of terms'

Doing some simple math, you get:

PMT = $23,606/[1-1/(1+0.002417)^60]

Solve and PMT = $423.12

Now we know:
Initial Loan Balance- $23,606
Interest Rate- 2.9%
Loan Term- 60 months
Payment- $423.12

In any given month, your interest due is the outstanding balance times the periodic interest rate.

In month 1, the outstanding balance is $23,606 (since you haven't made any payments) and the periodic interest rate is 0.2417% (2.9% / 12 months). Your month 1 interest charge is $23,606 * .002417 = $57.05.

If you pay $423.12 in month 1 and $57.05 goes to interest, then $366.07 goes to principal ($423.12 - 57.05).

In month 2, the outstanding balance is $23,239.93 ($23,606 - 366.07) and the periodic interest rate is again 0.2417%. Interest charge is $56.17. Principal is $366.95. New loan balance is 22,872.98.

And so on...
 
Originally posted by: sactoking
Sure, it's not too hard.

Here's what I know:
Initial Loan Balance- $23,606
Interest Rate- 2.9%
Term of the loan- 60 months

Using those three items, I can solve for your monthly payment using the present value of an annuity equation. The equation is:

PVA = PMT[1-1/(1+i)^n]

Where:

PVA is 'Present Value of the Annuity'
PMT is 'Payment'
i is 'interest per term'
n is 'number of terms'

Doing some simple math, you get:

PMT = $23,606/[1-1/(1+0.002417)^60]

Solve and PMT = $423.12

Now we know:
Initial Loan Balance- $23,606
Interest Rate- 2.9%
Loan Term- 60 months
Payment- $423.12

In any given month, your interest due is the outstanding balance times the periodic interest rate.

In month 1, the outstanding balance is $23,606 (since you haven't made any payments) and the periodic interest rate is 0.2417% (2.9% / 12 months). Your month 1 interest charge is $23,606 * .002417 = $57.05.

If you pay $423.12 in month 1 and $57.05 goes to interest, then $366.07 goes to principal ($423.12 - 57.05).

In month 2, the outstanding balance is $23,239.93 ($23,606 - 366.07) and the periodic interest rate is again 0.2417%. Interest charge is $56.17. Principal is $366.95. New loan balance is 22,872.98.

And so on...
Click to expand...


According to this site, the formula should be:

PMT = PVA * i / [1 - (1 + i)^(-n)]

From that, I got PMT
= 23606 * (0.0024166) / [1 - (1 + 0.0024166)^(-60)]
= 23606 * (0.0024166) / (1 - 0.865177)
= 23606 * (0.0024166) / 0.1348229
= 23606 * 0.0179243
= 423.12






 
If you want to see interest per payment, take the monthly interest rate, and convert it to a daily rate based on how many business days there are in that month (usually how it works, though the monthly interest could be smoothed instead).

It also depends on how it's compounded. For example, mortgages are compounded semi-annually (at least in Canada), so the monthly interest rate is (1+i/2)^(1/6), since there's 2 semi-annual periods in a year, and there a 6 monthly periods in each semi-annual period.

If the interest is APR, that generally means that the rate is the the effective interest rate. That would mean the monthly rate is (1+i)^(1/12)-1, NOT i/12, as if you use i/12 you get an effective annual interest rate of (1+i/12)^12 which is greater than i.

So your monthly interest rate is 1.029^(1/12)-1 = .002385
Figure out how many business days in the month. If there were 21 (average), you get 1.002385^(1/21)-1 = .000113443

Figure out how many business days since your last payment (x). Take your remaining principle at the beginning of the month (B) and your interest outstanding is [(1.000113443)^x-1]*B, and the rest of your payment goes towards principle.
 
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