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# when 0% interest is more costly..

Posted on 2015-02-21
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there is a scenario:
either 0% interest on loan for year but 5% fees.
or
8.9% interest on loan for 2 years.. but not fees.

what will be the cut-off in terms of months when the 8.9% will make more sense than the 0%. what will be the formula for determining that?
(example. if the loan will be paid back in 40 days, perhaps 8.9% is better? likewise, what is the crossing point in terms of months, when 0% becomes the better choice, in terms in savings on interest).

thx-
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Question by:25112
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LVL 97

Assisted Solution

John Hurst earned 860 total points
ID: 40623390
You can do a decent approximation as follows.

Work out 8.9% x amount of the loan and divide that by 24.  Call this monthly interest.

Now take the number of months x monthly interest and see how that compares to 5% fees.

Interest starts high and reduces as capital is paid back, but the above is a reasonable approximation to start with.
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LVL 97

Assisted Solution

John Hurst earned 860 total points
ID: 40623392
Here is an interest amortization calculator that allows you to print a schedule. Use something like this to get a more accurate answer. The approximation above is a simple and easy way to look at your problem.

http://www.bankrate.com/calculators/mortgages/amortization-calculator.aspx
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LVL 20

Assisted Solution

jmcg earned 284 total points
ID: 40623502
Time-value-of-money calculations can be tricky because you can't compare two different streams of payments scenarios without supplying your personal discount rate. For a short-term comparison like this, you might be able to get away with ignoring your discount rate, but for longer term comparisons it could become a serious error.

The discount rate that applies combines an estimate of your opportunity costs for funds, your tolerance for risk, and your plans for the future. Changing your discount rate can affect whether one loan choice is preferred over the other.

There's an NPV (net present value) function in Excel (and other spreadsheets) that you can use to model your two different scenarios, but you have to be careful when you introduce things like the initial fee or the idea of an uncertain early payoff date. For an example of how you might work out the details, it looks like this web page has good advice:

http://www.propertymetrics.com/blog/2014/09/30/how-not-to-use-npv-in-excel/

In summary, the 5% fee loan is likely a better deal if you expect to be able to pay off the balance in less than a few months.

But the whole thing is different if you are in a position to make someone else a loan where they're willing to pay more than 9% interest (before any risk premium). In that case, the 5% upfront fee is too much of a loss in terms of opportunity cost and you're better off taking the other loan (and loaning the proceeds out at 9%+).
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LVL 70

Assisted Solution

Merete earned 284 total points
ID: 40623637
Here in Australia if I pay off a loan ( contract) early I still pay a penalty fee for early exit. Go figure.
I paid out my car loan 2 years early and still got a hefty fee based on their contract finance details so it's a bit iffy which way to go.
Once they calculate all the % for a term even when paid out they still keep the % of that load.
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LVL 97

Assisted Solution

John Hurst earned 860 total points
ID: 40623767
I neglected a link in my post above. Fixed.

See http://www.bankrate.com/calculators/mortgages/amortization-calculator.aspx and down the page you can print a schedule.

Sorry for the inconvenience.
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Assisted Solution

dhsindy earned 284 total points
ID: 40623969
Used Math Lab calculator:
http://www.webmath.com/amort.html

They are very nearly the same.  A one year 0% interest 5% fee you repay 1050 for a 1000 loan.  For the 2 year 8.9% loan if you made 12 equal monthly payment instead of 24 the payoff would be 1048.92.

So, the 5% method would cost you about 1.08 units more over a one year term.  The banker is getting his roughly 5% percent either way.
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LVL 25

Accepted Solution

nickg5 earned 288 total points
ID: 40624267
Is the 5% a one time fee?
Is the 8.9% compounded as an APR - annual % rate?

Some interest compounds "daily" on the unpaid balance.

Some loans the interest is front loaded which means you pay more interest in the first series of payments be it 12 months or some other period. Then in the last few payments the interest is really low.

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I have a loan at 5.99%. It's an APR (annual % rate).
They calculate it each month. If my March payment is made on March 15 and the payment amount is \$195.00 they calculate the interest on the total unpaid balance, before applying my \$195 payment. Same thing repeats itself each month.

They receive my current payment. They hold it in their hand. They charge the interest accrued since the last payment and then they subtract my \$195 payment and send out the new payment notice end of the month.
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LVL 25

Expert Comment

ID: 40653059
The amount of the loan can be a factor. We are paying on a \$6,000 loan at 5.99% APR. That's \$359.40 a year or \$30 a month. It is worth it, regardless whether it is 3.99% or 5.99%. It will be paid off in one year so the term and the amount is not significant really.
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