Does compounding interest on a loan matter if you pay all the interest accrued each statement?

Question

Several answers on a question about recalculating interest when paying off a mortgage early mentioned how their examples didn't account for compound interest, which would complicate things. Is this true, though? Obviously compounding interest matters a lot when the interest is added to the principal of a loan. However, if we assume you are always making your payments on time, and they are enough to cover interest accrued that month, then does the frequency that the interest compounds matter at all? It seems to me that there would never be any interest to compound.

Clearly the case is different if your loan is in deferment, your payments are too low to cover the interest, or you neglect to make payments when due. I'm asking about things like fixed rate/term mortgages and car loans and you are keeping up with your payments.

Answer 1

Yes, it does. Let's say you borrow $10,000 with 1% interest a month (to keep the numbers simple) and you pay $120 every month. Because of compound interest, it doesn't matter if we count the $120 towards the amount borrowed or the interest paid, the interest for $10,000 is $100, so after a month you owe $9,980 and you pay interest on $9,980.

Without compound interest, you would deduct the $120 from the amount borrowed. So after a month you would owe $9,880 plus $100 interest, and you would only pay interest on the $9,880. So your monthly interest goes down by $1.20 every month, not by $0.20 initially.

But then show me a bank that doesn't charge compound interest. (Actually, Sharia law states that you cannot charge compound interest.)

Answer 2

If all your loan payments are the same size, then they have to exceed the interest on the loan. If they didn't, then you'd never pay off the loan, as the principal would grow rather than shrink.

Even so, compounding still matters. First, compounding at a frequency greater than that which you make payments will mean that you pay compounded interest with each payment. For example, if you pay monthly but your interest is compounded daily, your monthly payment will include your daily compounded interest. But even if the compounding frequency is less than the payment period, it still matters because it affects the principal. A quick example:

Principal Interest Payment
$1000     $3       $202
 $801     $2.40    $202
 $601.40  $1.80    $202
 $401.20  $1.20    $202
 $200.40  $0.60    $201

This is $1000 borrowed at 3.6% annually which is a monthly rate of .3%, compounded monthly. Now let's see what the same loan looks like without compounding.

Principal Interest Payment Accrued
$1000     $3       $202    $3
 $798     $2.39    $202    $5.39
 $596     $1.79    $202    $7.18
 $394     $1.18    $202    $8.36
 $192     $0.57    $200.93 $8.93

Not a huge difference with so little principal for such a short term, but measurable.

You might try to avoid compounding on a loan where interest is added to the principal with variable payments. Payments would look like

Principal Interest Payment
$1000     $3       $203
 $800     $2.40    $202.40
 $600     $1.80    $201.80
 $400     $1.20    $201.20
 $200     $0.60    $200.60

But note how we're back to paying $9 of interest, not the $8.93 of simple interest. Worse, the higher payments in the early periods are with more valuable current dollars while the lower future payments are in less valuable future dollars. This is the exact opposite of what you'd want to do.

The only way to avoid compounding is to pay off the entire loan before the second time that interest is charged. Otherwise it is still there, making the loan more expensive.