How to Calculate Interest on Long Term Debt

This is probably super boring for most of you but if you are reading this you must have some interest, no pun intended (OK maybe), in understanding how the interest you are being charged is calculated.  When we started paying down our debt it was important for me to understand the effect of our interest rates on our loans and it was eye opening.

Terms

Before we get started let’s review the terms involved so we are on the same page.

Principal Balance – This is the amount owed.  If you took out a $10,000 student loan then the amount owed simply would be $10,000.

Interest – This is a percentage that is charged to the principal balance and is basically the fee for borrowing the money.  The lower the interest the better for you.

APR – This stands for ‘annual percentage rate’ and is directly related to the interest charged.  It means that the interest rate is charged on an annual (yearly) basis.

Minimum Payment – The required monthly payment as determined by the loan company to stay in good standing and is determined by the payoff period.  Any interest charged that month will be paid off and the remainder goes to principal.

Payoff Period – This is how long it takes to pay off your loan.  This is typically 5 years for a car loan, 10 years for student loans and 15 or 30 years for mortgages.  The longer the payoff period the lower your minimum payment is but you end up paying more interest in the long run.

Now that we know the terms let’s get into the math.

We’ll assume the following figures for our examples:

Principal Balance – $10,000

Interest Rate – 5% (also can be written as .05)

Minimum Payment – $100

*Note, if you were paying this on a true 10 year period your minimum payment would be $106.07.  To simplify things I am rounding that to $100 for these examples.

Two Methods

There are two ways to calculate the interest and that is determined by the lender.  The first, and more common way, averages the interest over 12 months as payments are typically due on a monthly basis.  The second way is more specific and determines the amount accrued on a daily basis.  Either way, at the end of the year you pay the same amount regardless of method.

I suggest you look at some of your loan statements and see how much interest is charged.  By plugging your numbers into these simple calculations, you will be able to determine which method is used.

Method 1

Take the principal balance ($10,000) and multiply that by the interest rate (.05) and divide that amount by 12 since there are 12 months in a year.  Here it is written in the formula.

(principal x interest) / 12 = interest accrued per month

($10,000 x .05) / 12 = $41.67 interest accrued

Based on that you would pay $41.67 in interest for that month.  Every month will be different since the principal balance changes every month after a payment is made.  If you make your monthly payments it will go down.  If you miss payments and let interest continue to collect your balance will go up.  Avoid that at all costs.

Method 2

This method takes into account the amount of time that has lapsed (in days) between payments.  Let’s assume a full 31 day month has passed between payments for this example.  Most likely though it will vary each month and could be as little as 20 days or 40 days depending on when you make your payment each month.  My Sallie Mae loans were calculated this way.

Take the principal balance ($10,000) and multiply that by the interest rate (.05) and divide that amount by 365 since there are 365 months in a year.  Here it is written in the formula.

(principal x interest) / 365 x days between payments = interest accrued per month

($10,000 x .05) / 365 x 31 = $42.47 interest accrued

Based on that you would pay $42.47 in interest for that specific month.  You’ll notice that it is a little higher than the first method.  Don’t freak out and think you are getting charged more.  You might be for that 31 day month but if it had been a 30 day month or February (28 days) you would pay less if you use those numbers in the calculation.  The key point to notice is that method 1 basically takes an average of each month and method 2 gets more specific.  At the end of the year you pay the same amount overall.

You also don’t have a choice in how the interest is calculated but it is good to understand how it is calculated for your next statement.

Minimum Payments

When making a payment, the interest accrued is first paid off entirely and the remaining payment is applied to the principal balance.  The amount left over is the remaining principal balance and interest will start to accrue on that amount and so on and so forth each month.

Let’s plug our numbers in to see it take shape.  I am using Method 1 in these examples to calculate the interest.  As a reminder, the minimum payment is $100 a month and the accrued interest is $41.67 as stated above.

MONTH 1

$10,000 + $41.67 (interest accrued) = $10,041.67 – $100 (minimum payment) = $9,941.67 (new principal balance)

Once the payment in made the interest is paid off entirely and interest starts to accrue again based on the new principal balance.  Let’s calculate it for month 2.

MONTH 2

($9,941.67 x .05) / 12 = $41.42 interest accrued

You’ll notice that the amount is a little lower than the first month of interest accrued.  If you just make the minimum payments then it will go down steadily each month like that but you will pay the maximum amount of interest over the life of the loan.

The other thing you’ll notice is that while you paid $100 your loan balance only reduced by $58.33.  That is the toll that interest takes on you.  The interest that you pay does nothing to help your remaining principal balance and in turn means that you will pay much more than $10,000 over the life of the loan.

So, what happens if we pay extra?  How much can we save?

Extra Payments       

If, for instance, you paid an additional $1000 a month how would it affect your balance?

MONTH 1

$10,000 + $41.67 (interest accrued) = $10,041.67 – $1,100 (minimum payment + extra) = $8,941.67 (new principal balance)

By paying an extra $1000 you see how much lower your principal balance ends up.  As that lowers the interest charged the next month lowers as well.

MONTH 2

($8,941.67 x .05) / 12 = $36.26 interest accrued

So, by paying the extra amount you have lowered the amount of interest being charged each month.  It is the same interest rate, but there is less principal to charge interest to.  Now, don’t be fooled and think that by paying extra you have only saved $5.  No, what you have done is also reduced the overall amount of time required to pay off the loan and each time you pay extra you drastically cut off months of your overall payoff period.

How do we know this?  We can use an amortization schedule to calculate out how much we would pay overall.  An amortization schedule lists out each payment that you make and shows the amount of interest paid.  If you have a mortgage it is possible that they printed one for you when completing your loan.

Click here for a loan calculator and amortization schedule.

Over 30 years you would make 360 monthly payments (30 x 12) on a mortgage if you never made an extra payment.  For a typical 10-year student loan you would pay 120 monthly payments (10 x 12).  By not paying extra, you are putting yourself in a position where you pay interest on 360 or 120 payments depending on the loan.

If we pay extra we not only reduce the amount of interest you pay on the next payment, but you also reduce your payoff period going forward.

If we go back to our examples let’s see how much we would pay if we just paid the minimum each month and how much we can save by paying extra.

How Much Can We Save?

As stated earlier, if we pay the minimum on a 10-year loan we pay 120 total payments.  That means 120 payments where interest is being charged.

Per the amortization schedule you would pay $12,966.25 total on a $10,000 loan.  That means that you paid $2,966.25 in interest over the life of the loan.  That is the fee for borrowing the money.

It doesn’t have to be that way though.  You can reduce that amount significantly.  Going back to our extra payment if we paid an extra $1,000 a month you already know that it will take less than a year to pay off.

By adding that $1,000 a month the amortization table tells us we’ll pay $10,216.65 total.  That is only $216.65 in interest.  That saves us $2,749.60 in interest!  It also means that we will pay it off in 9 months.  Think about that, you save $2,749.60 and pay it off in 9 months.  That is a huge savings in time and money. That is how you buy freedom!  That makes it worth not eating out or waiting to take that vacation.

If you hate dealing with your lender, paying off your loans early is a great way to stick it to them.

After you pay it off you now have that minimum payment back and could put it anywhere.  If you follow the Debt Snowball method you would simply apply it towards the next debt but you have one less commitment to pay that next month.  How great is that?!

Our Loans

So how did us learning how interest is calculated affect our loan payoff?  Well, I learned that if we just paid the minimums we would pay $50,000 in interest and be paying into my 50’s.  We’d be finishing up my student loan payments as our son is starting college.  That was a huge motivation to avoid that situation.

By paying off our $107K of loans in 33 months we saved $40,000.  That is $40,000 that we can now invest and have earn money.  Once you understand that you can see how detrimental debt can be.  You’re not only paying interest but you are losing out on the potential interest you can earn with your money if you invested it.

Conclusion

I know this was a long post but I hope it helps break down how you can develop a deeper understanding of your loans and use that as motivation and a tool to pay them off sooner.  Simply put, the more you pay each month, the more you save next month.