Citibank Student Loans and Daily Compound Interest

My wife has significant student loan debt from her time in law school. Not only was she paying tuition, but she had to pay living expenses to live in NY for three years, all paid for with loans. While I was really starting to track our finances, I began taking a longer look at our loan payments to track exactly how much we owed. It took me weeks to figure out what was going on, and since I bet we're not the only ones to be confused, I thought I'd try and explain it here to save others some trouble. I'll try and give the story without using the real numbers, but it will be tough.

We have 4 student loans, all services through Citibank:

  1. A federal loan, 3.5% fixed, $30,000
  2. A federal loan, 3.5% fixed, $30,000
  3. A small private loan, 4.5% variable, $10,000
  4. A large private consolidation loan, 7.75% fixed, $100,000

The key here that we failed to fully realize, is that all of these loans compound their interest daily, not monthly like all our other loans (mortgage, car, etc..). But more on that later.

The large consolidation loan is relatively new, as we just consolidated last year from variable rate loans from another services to the fixed rate at Citibank.

Citibank has lumped these four loans into two payments. The federal loans are grouped into account "-70", and the consolidation and smaller private loans are lumped together in into another payment to account "-72". The minimum payments we've been given are (again, made up numbers, but proportional): $250 for account -70, and $800 for -72 ($700 for the consolidation loan)

We've been making the minimal payment for the past several months, so imagine my surprise when I went to enter the loan into kmymoney earlier this year, and *the principal on our consolidation loan hadn't gone down, not one penny*. Where had our money gone?

Deciphering the Citibank Statements

The first clue as to where the money was going figuring out how to decipher the Citibank bill. Most other bills we get tell us exactly how much we own on the loan, and call it the "balance". However, Citibank does things differently. They list -two- balances. One labeled "Principal Balance", and the other is the "Payoff Balance". Our principal balance was still the full original loan amount. The payoff balance was listed as the "balance if paid on due date".

Normally, I would think that the payoff balance would be the principal balance plus all the amount of interest gained in the month. $100,000 at 7.75% fixed interest should earn about $645 in a month ((.0775/12))*100.000 = ~$645. But our payoff balance was higher, somewhere around $101,000. That wasn't right. Several calls to citibank later, and we finally figured out what happened.

First, understand this: No where on Citibank's statement do you find the exact amount (principal + interest) that you owe. They say this is because interest is compounded daily, and so the actual amount you owe changes each day. I don't see why they can't just say "as of this date, this is what you owe", but whatever. So, instead, they give you what you owe on the loan (principal balance) and what you would pay if you paid it off on the due date of the statement (payoff balance = principal + interest accrued this month). Ok...

But the number still weren't adding up for us.

Citibank drags out sending their initial bill

The other clue, looking at past statements, they showed that our entire payment each month going to interest. That's odd. Payments should be going towards interest AND principal. But every payment from the start went only to interest.

Our consolidation loan went through on may 31st, 2008. But by the time the check was cashed by the other servicer, and with Citibank shuffling their feet, we didn't get our first bill until July, and it didn't get paid until August (when it was due). And therein lies the problem. Our loan has accrued nearly two months of interest, before we made a single payment. I'm not 100% sure this was legal, but whatever.

Since Citibank doesn't have a spot on their statement that shows how much interest you've accrued, the only way this shows up is that the payoff amount is higher than it should be. That's what happened. We had accrued a lot of extra interest because of the lab between when the loan went through and when the first bill got paid. All of our payments since were going towards paying down that extra accrued interest, which was not clearly spelled out on the statement.

Why did it take us 6 months and we still hadn't paid off the extra interest?

Citibank's "minimal payment" is very, very, minimal

The final piece of the puzzle is the minimal payment that Citibank quoted us. It took us a long time to realize what a "minimal" payment means when you talk about daily compound interest. The principal + accrued interest is different depending on not only when you pay your bill, but when you paid your last bill. If you have a $100,000 loan, then every day you're accruing ~$22 dollars a day ( (0.0775/354)*100000 , and this ignores accrual). Lets say you get your bill on the 20th, and it's due on the 30th. | If you pay your bill exactly on the 30th, when the next month pay again on the 30th, then you've accumulated 30 days worth of interest.

But now lets say the next month you pay when you get the bill on the 20th. Now you've only accumulated 20 days of interest, and if you make the same payment it'll go a lot further (more of the payment goes to principal, not interest). But if the next month, you pay on the 30th again, then you've now accumulated 40 days worth of interest.

Citibanks minimal payment, as far as I can tell, is tuned for a little less 30 days between payments, and a tiny bit towards principal above that. So if you pay irregularly, and some months pay at a larger interval (40 months), your minimal payment will not be enough to cover the amount of accrued interest. In other words, you can make your "minimal payment", and still have the amount you owe go up.

Over the life of the loan, most long months will be balanced out by a short months, but it's still quite a shocker wen you're used to dealing with monthly interest accrual where you you can make your payment anytime within the payment window and be guaranteed how much goes to interest versus principal.

In my mind, the minimal payment should be the minimum needed to guarantee that no matter when you make the payment, your payment goes down. But that's not the case.

Spreadsheet

After gathering all the information, I've created a spreadsheet in openoffice which takes the current balance of the loan, the interest rate, and the date the last payment was credited to the account, and returns how much interest has accrued for each day (including accrual). It's not exact, but it gets within a buck or two what really happens on the loan, so it's pretty close. If people want, I'll clean it up (and clear out my real loan data) and post it here. With it, you can tell if you minimum payment will really be enough to cover the interest you've accrued since your last statement.

Conclusion

So, I finally have a handle on how the loans work. It's very confusing, and Citibank seems to be going out of its way to make things confusing, but you can get through it. I've upped our payment and now we pay much more than the minimum and are taking decent chunks out of this loan with each payment. We're still a long way from paying it off, but at least now we understand what's going on.

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