It's got an awesome appetite: Tyrannosaurus Debt
February 28, 2008 12:05 PM   Subscribe

How do you figure out daily interest from an APR on student loans due monthly?

I have about 100k USD in student loan debt, at a fixed APR of 5.75%. I wanted to work out what the monthly rate was, but my debt holder tells me that the interest is actually calculated daily, though the payments are due monthly. Then they sent me twenty pages of amortization tables, I suppose imagining that it would help me somehow. Aside from seeing that 75-80% of each month's payment goes to interest before any of it goes to principal, the tables don't help me.

I accrue and pay off a small amount of credit card debt each month, mostly in grocery bills. This is deliberate, since it's a monthly expense I'd have anyway, and paying by credit instead of debit is (I think) at least a slight help to my credit score.

I have no other debt.

I can see conceptually that paying as much extra as possible as soon as possible is best for reducing the total amount paid on this debt.

What I'd like is to work all of this out into a big spreadsheet so that I can see the actual final result of any extra payments made.

How do I do this? I feel like maybe I'm venturing into the realm of deep magic.

I've poked around in the archives here and not found another question asking this; if I've missed it, a pointer would be great.
posted by johnofjack to Work & Money (8 answers total) 4 users marked this as a favorite
Response by poster: I forgot to mention: prepayment is allowed.
posted by johnofjack at 12:07 PM on February 28, 2008

Best answer: The daily rate will be equal to the yearly rate (APR) taken to the 1/365. So if your yearly interest rate is 5.75%, or 1.0575, then you can get your daily interest rate in excel with the formula:


which comes out to be about 0.000153, or 0.0153%. (Excel rounds a bit in its calculations, so it's not perfectly precise.)

I actually did a spreadsheet that showed almost the exact same thing to motivate myself to pay off my student loans after I graduated college. What I personally found very motivating was just the actual dollar amount of interest I was paying every single day that I had the loan. Every time I paid down my principal, that number would drop to a less horrifying level. It started at about $5 a day (man, that was *depressing*) then dropped to $3.50 after I had paid off some big chunks of it (still equal to a Starbucks latte every day) then down and down until it was zero. Every day I would look at that number and think of something I could buy with that wasted interest--a beer at happy hour! an overpriced coffee! a chocolate bar after lunch!--and it helped kicked my ass into super-saver mode.

If that would be useful, you can just set up a sheet so that your principal is in one cell (this will change every time you make a payment), your daily interest rate (in your example, 0.000153) in another, and the third being the product of the two. Assuming I haven't made any math errors, you're currently paying a bit over $15 every day in interest.
posted by iminurmefi at 12:33 PM on February 28, 2008 [1 favorite]

Best answer: you could use a mortgage pre-payment calculator, such as this one which shows the difference if you make your payments bi-weekly.
posted by ejaned8 at 12:34 PM on February 28, 2008

Response by poster: The daily rate will be equal to the yearly rate (APR) taken to the 1/365.

Is it really that simple? I was asking all the wrong questions on the phone, then, and they weren't just trying to be cagey.
posted by johnofjack at 2:23 PM on February 28, 2008

Response by poster: Hm, it's either a rounding error or the miracle of compound interest, but using a1 = 100000
; b1 = 0.000153 ; c1 = a1 + (a1*b1) ; and a2 = c1 puts the total $9 off over the course of a year. Still, I'm not a bank and this doesn't distress me greatly; it's close enough to get a good idea of the long-term results of small immediate actions. Thanks, iminurmefi (answrn ur ax).
posted by johnofjack at 4:44 PM on February 28, 2008

The rounding error is in the .000153 number that you're using. Fill in that field with: =5.75/365 to get the full precision
posted by chrisamiller at 4:53 PM on February 28, 2008 has over 250 free financial calculators and they have that capability to plug in an extra amount on just one payment on an amoritized payment, or maybe one extra payment here and there of varying amounts. The site is extremely thorough and should be able to give you the chart of your dreams.
posted by 45moore45 at 5:17 PM on February 28, 2008

Response by poster: Ah, thanks for the suggestions. chrisamiller, I replaced the percentage with =(1.0575)^(1/365) and then changed C2 to =A2*B2 and that took care of it.

45moore45, that looks like a very thorough site but the calculators don't show up for me. Maybe it's because I've turned off Java (the computer's slow enough already)...
posted by johnofjack at 4:54 AM on February 29, 2008

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