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I have an auto loan for $14414.00 at 12.5% for 72 months.

If I pay $96 every 10 days, how fast will I pay it off? Does this strategy make any difference?

  • 3
    Does your loan contract say that partial payments are held (without interest) until a full payment is available? Or do early partial payments reduce your interest? – Jasper Sep 15 '17 at 4:01
  • 3x96 per month is just about what the monthly payment should be, maybe a couple bucks over, so unless they apply partial payments as they are received you wouldn't pay it off any faster. If you can pay more than the monthly you can save a nice chunk of interest. – Hart CO Sep 15 '17 at 4:08
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It all depends on your loan contract, and the way most are written, the 10 day thing will not help. However, assuming that the contract is written in such a way to allow this, the difference will be negligible.

By "saving money" I assume you mean the amount of interest paid.

There is really two ways of doing this. If you carry the loan to term paying the indicated amount on the due date you will pay $6,140 in interest. An increase of over 33% to the cost of the car. Yikes, that is a lot of money. You should seek to minimize your interest expense.

One way to do this is to reduce your rate. Applying for a new loan that is at a more reasonable 6% and continuing to pay the ~285 per month will reduce the term to 59 months and only cost you $2,245 in interest. A large savings.

Even better is to work a second job and earn an extra 1,000 per month. Then bundle it with your 285 payment and shoot that at the loan. This way you will only pay $965 in interest, and have it paid off in a year. Once you do that, you can stick $300/month or so in a savings account or other investment and pay for every other car in cash. Making choices like these leads to building wealth.

So the question becomes do you want to spend the rest of your life on the hamster wheel of car payments, or do you want to spend one year in pain so you make smart choices in the future? The choice is yours.

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Using the following loan equations where

s is the principal
d is the periodic payment
n is the number of periods
r is the periodic interest rate

enter image description here

∴ d = r (1 + 1/(-1 + (1 + r)^n)) s

and

n = -(Log[1 - (r s)/d]/Log[1 + r])

With the balance b[n] in period n given by

b[n] = (d + (1 + r)^n (-d + r s))/r

Applying the OP's figures

principal, s = 14414
interest rate, r = 12.5/100/12
number of months, n = 72

monthly payment, d = r (1 + 1/(-1 + (1 + r)^n)) s = 285.558

total interest = n d - s = 6146.20

Check & demonstration

number of periods, n = -(Log[1 - (r s)/d]/Log[1 + r]) = 72

balance in period n, b[n] = (d + (1 + r)^n (-d + r s))/r = 0

Switching to $96 payment every 10 days, with 365.2422 days per year

annual effective rate, a = (1 + r)^12 - 1 = 13.2416 %

10 day periodic rate, r = (1 + a)^(10/365.2422) - 1 = 0.00341049

periodic payment, d = 96

linear repayment periods = -(Log[1 - (r s)/d]/Log[1 + r]) = 210.764

whole periods, n = 210

enter image description here

balance remaining in period n, b[n] = (d + (1 + r)^n (-d + r s))/r = 73.10

so the repayment in period 211 is smaller than usual, b[n] (1 + r) = 73.35

total interest = n d + b[n] (1 + r) - s = 5819.35

interest saving = 6146.20 - 5819.35 = 326.85

repayment time = 211*10*12/365.2422 = 69.3239 months

Paying $96 every 10 days saves $326.85 and pays the loan down 2.68 months quicker.

  • This answer assumes that partial payments reduce the average daily balance that is used for calculating the interest each month. This assumption allows an extra principal repayment of about one dollar per month. This difference in assumptions is the reason for the difference between this answer of about 211 10-day periods, and my estimate of about 212 10-day periods. Both answers assume that the borrower is not charged any late fees if they only make two partial payments during the month of February. (Many loans have a five day grace period, so this shared assumption is often correct.) – Jasper Sep 21 '17 at 4:14
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You'd have to check the terms of your contract. On most installment loans, I think, they calculate interest monthly, not daily. That is, if you make 3 payments of $96 over the course of the month instead of one payment of $288 at the end of the month (but before the due date), it makes absolutely zero difference to their interest calculation. They just total up your payments for the month. That's how my mortgage works and how some past loans I've had worked.

All you'd accomplish is to cost yourself some time, postage if you're mailing payments, and waste the bank's time processing multiple payments.

If the loan allows you to make pre-payments -- which I think most loans today do -- then what DOES work is to make an extra payment or an overpayment. If you have a few hundred extra dollars, make an extra payment. This reduces your principle and reduces the amount of interest you pay every month for the remainder of the loan. And if you're paying $1 less in interest, then that extra dollar goes against principle, which further reduces the amount you pay in interest the next month. This snowballs and can save you a lot in the long run. Better still, instead of paying $288 each month, pay, say, $300. Then every month you're nibbling away at the principle faster and faster.

For example, I calculate that if you're paying $288 per month, you'll pay the loan off in 72 months and pay a total of $6062 in interest. Pay $300 per month and you'll pay it off in 67 months with a total of $6031 interest. Okay, not a huge deal. Pay $350 per month and you pay it off in 55 months with $5449 interest. (I just did quick calculations with a spreadsheet, not accurate to the penny, but close enough for comparison.)

PS This is different from "revolving credit", like credit cards, where interest is calculated on the "average daily balance". With a credit card, making multiple payments would indeed reduce your interest. But not by much. If you pay $100 every 10 days instead of $300 at the end, then you're saving the interest on 20 days x $100 + 10 days x $100, so 12.5% = 0.03% per day, so 0.03% x ($2000+$1000) = 90 cents. If you're mailing your payments, the postage is 49 cents x 2 extra payments = 98 cents. You're losing 8 cents per month by doing this.

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Assuming that partial payments are held (without interest) until enough money has accumulated to make at least a full payment, and assuming that overpayments are applied toward principal, a strategy of making three $ 96.00 payments per month will shorten your amortization period by less than one month. These calculations assume that the interest rate is 12.5 percent APR, compounded monthly (with an APY of 13.2416 percent).

Instead of 71 payments of $ 285.56 plus a final payment of $ 285.38, you would make the equivalent of 71 payments of $ 288.00 plus a final payment of $ 28.10.

If you make one $ 96.00 payment every ten days, you will make an average of 36.5… partial payments per year, instead of 36 partial payments per year. This will speed up your loan amortization by about another month-and-a-half over the course of the 72 month loan. One month of shortening is due to the extra principal payments, and the other half-month is due to interest savings. To a second approximation, this strategy is similar to paying $ 292.00 per month for 69 months plus a final payment of $ 195.38. In other words, this strategy will probably involve about 212 payments of $ 96.00 each, possibly with a small 213th payment.

  • Another question about a "monthly payment discrepancy" uses the compound interest formula for relating the monthly payment to the initial principal balance. – Jasper Sep 15 '17 at 4:20
  • If you calculate the initial value of a loan using a round number for the monthly payment amount, your answer will not quite match the initial principal amount. This discrepancy can be compounded for the life of the loan, to calculate the amount by which the final payment is less than the required average monthly payment. An answer about how term reduction is calculated explains how to calculate the savings at the end of the loan from making an extra payment early on. – Jasper Sep 15 '17 at 4:30

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