Is My Math Right on This Loan Scenario?

Question

Two years ago, I borrowed money from an investor which I used towards a down payment on a 20-unit apartment complex. Terms on the loan were:

Amount: $100,000

Rate: 8.0%

Amortization: 25 years

Scheduled monthly payments are $771.82. However, my properties have done well and I’ve been aggressively paying down extra principal on this loan. Current remaining principal balance is $62,178.13.

Here is my question. I just sold one of my other apartment buildings and have a nice chunk of cash. I’m planning to buy another property but it will likely take a while to find the right one. I was considering paying down this loan, with the thought process that paying down an 8% loan is comparable to earning 8% somewhere else. However, when I ran the numbers I came up with some come conclusions I didn’t expect. Maybe I’m doing something wrong so I wanted to run it by this group for some help please.

If I paid off the loan today, I will have paid around $15,245 in total interest in the 25 months of payments. Dividing $15,245 by $100,000 and further dividing by 2.0833 gives me the annual interest rate right? That comes to 7.318%. So if I pay the remaining balance off today, the actual interest rate I paid would be 7.318% right?

The option on the other extreme is to just pay the minimum payment for the remainder of the loan term. The total interest I would pay in that scenario is around $42,113 in 300 months of payments. Dividing $42,113 by $100,000 and further dividing by 25 gives an annual interest rate of 1.685%. So if I start paying only the minimum from now on, I am lowering my effective interest rate and will eventually only have paid 1.685% annual interest? Can that be right?

Am I missing something here? Unless I did the math wrong or am I reaching the wrong conclusions, it would seem the obvious choice is to just start paying the minimum. What am I missing? What would you do in my shoes?

Theo Z. · Answer

Wayne and Frank: thank you both for taking the time to respond. Your points make a lot of sense. I was looking at the situation from a long-term standpoint and that was blinding me to the fact I will always be paying 8% on current balance.

I'm still having a hard time reconciling this fact with why my long-term calculations of average interest rate paid are so low, but at least  I understand now that this calculation is not actually a legitimate one to be considering.  So thank you again for your help! It is much appreciated and has helped me make the decision to pay down most of the remaining balance on this loan since it is my debt with the highest rate by far.

Frank Jiang · Answer

Not in the slightest.  If you have made extra principal payments, you must change your interest/loan amount denominator to incorporate those additional principal payments, with consideration for time-value of money.  You are effectively paying $14,824 in interest on $100,000 - 33,354,50 in principal.  You are changing your loan amount by paying off principal, so you can't simply calculate your new interest by the original loan amount.

As Wayne stated, at the end of the day when you pay money towards a loan with an interest rate of 8%, you are yielding 8% on your money.  Your total interest amount has lowered due to additional principal payments, but your interest rate has not changed from 8%.  The only change is that the 8% is now yielding on a smaller principal balance.  If you are using a mathematical calculation that results in something other than 8%, it means the model is wrong.

Frank Jiang · Answer

You've definitely stumbled in your math.  In month 25, you should have paid 16,445.21 in cumulative interest.  You cannot simply divide your final interest / original loan number by 25/12 because that would ignore monthly compounding.

If you pay the loan off today, you are essentially paying yourself exactly 8%.

If you simply pay the 771.82 every month, the total interest you pay would be $131,544.87 (1.3x your original loan)

Unless you have another existing project that pays you more than 8% interest, your default best option is to pay off this loan.  The only options I would consider here are:

1) Payoff loan

2) Refinance with bank to a more reasonable rate

How to create an amortization table:

http://www.wikihow.com/Prepare-Amortization-Schedu...

Theo Z. · Answer

Andrew, I don't know how to link your name to my post above! Hopefully you still see it! Thank you again for taking the time to write

Andrew Postell · Answer

@Theo Z. I am following you on the math but I think it's really a philosophical investing question that you need to address.  What I mean is that some investors feel that as long as they cash flow on a property then it doesn't matter what the payment is because someone else is paying it.  Others feel that they always want cash in the bank to find more deals.  Some people believe that they only pay down their properties with the cash flow of other properties.  And some people just get really stressed out when they have debt.  Numbers aside, what is important to you? If you said, "Andrew, the numbers ARE what's important to me" then logically you should never have debt. But I think there's a threshold in there for you where a certain amount of debt is reasonable. A private loan has a lot of benefits - it's not on your credit report so it doesn't affect your DTI, it's probably more flexible if something really drastic were to happen to you and you needed some breathing room for a few months.  So there are reasons to keep it besides just the rate of interest.  Hope this helps some with your decision making.

Theo Z. · Answer

Thanks Frank. You're right that I would have paid $16,445.21 in interest after month 25 if I had not made any extra principal payments. However, over the course of those 25 months, I've paid $33,354.50  extra towards principal. As Stephanie said above, this has lowered my interest and is why I've only paid $14,824 in interest through month 25. You're also correct that the total interest I would pay over the course of the loan would be $131,554.87 if I never made any additional payments towards principal. However, give all the extra principal payments I've already made, if I just started paying the minimum each month from now on, I calculate that the total interest I will pay is $42,113.

Does this information change your recommendations?

Stephanie Medellin · Answer

@Theo Z.

You're only paying interest on the remaining balance each month.  Each month the portion going toward interest gets reduced, because you're paying interest on a slightly smaller balance.  That's probably why it's a little off.

Theo Z. · Answer

@Andrew Postell, thank you so much for the insight. My investing philosophy is I want my money to be working as hard as possible. My thought was that using money to pay down an 8% loan was essentially earning me an 8% return with very little risk. If that was the case, I'd be good with putting my money to that use. But when I ran the numbers it looked like it would only possibly save me less than 2%, which is a terrible return and that money would be better employed elsewhere.  I like debt as long as it's arbitraged and is making me money.

If my conclusions are right I will plan to just start paying the minimum. Ultimately, it sounds like you're saying my math is correct and I'm not missing something important? Is that right? I greatly value your insight on this. As a lender, I'm sure you look at this through a much more sophisticated lens than I'm able to.

Theo Z. · Answer

Thanks Wayne. I used a loan amortization calculator to determine the total interest paid. 2.083 was used to convert 25 months of interest into an annual rate. If it was only 24 months I would have divided by 2. Does that clear that up? How would you determine the actual interest rate for each scenario in order to make the best financial decision?

Is My Math Right on This Loan Scenario?

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