Analyzing the Prepayments on One of My Student Loans

As I made my monthly payment the other day on one of my student loans I wondered how much I have saved in interest over the years by adding to the principal some months.  Since the lender didn’t provide me with that information I almost looked at it as a challenge to see whether I could figure it out.  Since I had the drive to figure out the math problem and this blog so I had people to share the information with I went for it.

What is an Amortized Loan?

Before getting to my particular situation one would first need to know how an amortized loan works.  Investopedia defines an amortized loan as,

A loan with scheduled periodic payments of both principal and interest. This is opposed to loans with interest-only payment features, balloon payment features and even negatively amortizing payment features

Whether you know it or not, most people are familiar with the concept of an amortization table or schedule if you have a traditional 30 year mortgage or a car loan.  Every month when you make your payment the bank is automatically splitting the payment according to a mathematical schedule between principal and interest.   An amortization schedule allocates a disproportionate amount of interest to the early payments and then by the last payment you make it is almost entirely made up of principal.

• Interesting side note: When someone says a mortgage “forces you to save” it has to do with the concept we are talking about today.  As you  make your standard monthly payment part of it (not much at first as we homeowners know all too well) is paying down part of the principal.

What happens when you make an extra principal payment on an Amortized Loan?

Since on a traditional amortization schedule payments do not change when you make an extra payment your next monthly payment should not change.  I learned that lesson the hard way when I was prepaying my auto note and the payments were not being applied to principal but rather pre-paying interest! When you make an extra principal payment it should reduce principal on the back end, when that occurs the interest on that last payment should also disappear.  Lets take a generic example:

• $20,000 Note
• 60 Month Pay off
• 5% Interest Rate

This gives us a payment of $377.42/month, however, as we discussed before each payment will be made up of differing principal and interest amounts.

Your payment doesn’t change but the interest per month goes from $83 in the first month to $1.57 and the principal payments go from $294 to $376 (you may have to click the pictures to zoom in).

Now lets add an extra $50/month to our payments:

You may have to zoom in to see the numbers clearly, but what is happening is that all those extra payments are going to the later payments effectively erasing those later interest payments.

In the above example paying an extra $50 saves 7 months of payments and $352 in interest payments.

Prepaying my Student Loan Debt

Like I said my lender doesn’t provide my amortization schedule so I had to create one and then subsequently enter each payment for the past few years. While it is based on the mathematical formula that makes up a traditional amortization table I was shocked how close I got to the actual balance (under $50) considering there are different payments times, mistakes made by myself on servicing the note and even a change in the note holder.

First and foremost, I should mention that the debt is not large in terms of my total school debt.  I think my obsession with the note is that it is not a large balance and by finishing it up I would have one less bill to worry about and provide a $1,200 raise if I didn’t have to service the debt.  What do I mean by raise? See my favorite thing about paying off debt.

The terms of the note for this exercise:

• 10 Years
• 5%
• $10,000
• Payment of $106.07 – First payment was in February of 2007
• If I just paid the minimum for 10 years I would pay a bit over $2,200 in interest

Should I choose to just continue to make the minimum payments I would have 2+ years to go effectively eliminating 3 years of payments and saving over $500 in interest:

Since I have the spreadsheet built I ran some other calculations:

• To finish up the note by the end of the year I would need to pay $675/month.  This would save me a total of $648 on the total interest
• To finish up the note by the end of 2013 I would need to pay about $190/month.  This would save me a total of $587 on the total interest

I don’t think I could pull the trigger on sending $675/month on a tax deductible note which is only at 5%.  That being said, I think I am going to start shooting for around $200 doubling my payment so I can finish it up late next year.

Ever run this exercise before?