A Faster Way To Calculate Effective Annual Rate With Your HP 12c Platinum
HP12c is so unloved. All CFA candidates I know seem to be using TI BAII Plus. Schweser Notes even says it right out: “If you don’t already own a calculator, go out and buy a TI BAII Plus!”
If you see the examples in Study Session 2 of the Schweser Notes, it’s full of sentences such as “On the TI, enter…”
Darn RPN haters. Sigh.
Calculating EAR by following the formula
Anyway, today I’d like to share a shortcut that I had learned before encountering the Schweser examples on computing the Effective Annual Rate (EAR). The concept itself is quite straightforward: if a quoted annual rate of X% is compounded more than once annually–let’s say quarterly–then the effective annual rate is actually higher than X%.
The formula given is:
EAR = (1 + periodic rate)m – 1
So in one Schweser example, where the stated annual rate is 12% and it’s compounded quarterly, it goes like this:
- Compounding period is 4, so periodic rate is 12%/4 = 3%.
- Realize that 3% = 0.03, so to calculate the EAR following the standard formula, in HP12c we should type this:
1.03 [ENTER] 4 [yx]
- Which, on default settings in HP12c, gives the result of 1.13, since by default the calculator displays to two decimal places.
- Then we need to remember to subtract 1 from it, and realize that 0.13 is 13%, which is the effective annual rate.
- Except we realize that the answer given in that Schweser example is 12.55%, which is pretty bloody different from 13%.
So troublesome. Here’s a much faster and straightforward way to do it in HP12c–I suspect you can do it on TI BAII as well (note the slash “/” is used to represent the division key):
12 [ENTER] 4 [n] [/] [i] [CHS] [PMT] [FV]
Which I’m happy to report displays exactly 12.55.
Why does this work?
Let’s think for a while why this works. Here, instead of manually converting figures in percent to decimal, adding 1, raising to the mth power, subtracting 1, and converting it back to percent, we’re turning this into a simple TMV calculation.
That is, when we type in:
12 [ENTER] 4 [n] [/] [i] [CHS] [PMT] [FV]
we’re doing these steps (see the picture below, too):
- setting 4 as compounding periods (n)
- setting 3% as the periodic rate (i)
- -3 as periodic payment (negative means money that is paid out by us).
- calculating the Future Value (FV), which turns out to be the EAR.
So… why does this work? This works because this is the exact calculation that happens when we limit our calculation just to the interests alone, taking the original present value (assumed at $100 in this shortcut–remember that 3% out of 100 is 3 dollars) out of the calculation.
That is, this calculation answers the following question: “Let’s say I put in $100 now. From now onwards, every 3 months, the bank is going to pay me 3% interest on the principal, which will be added back to the principal. At the end of 1 year, how much interest will the bank have paid me?”
The answer is $12.55, which, for a principal of $100, means an effective annual rate of 12.55%.
January 28th, 2009 at 3:33 am
Great! Thank you!
I always wanted to write in my blog something like that. Can I take part of your post to my blog?
Of course, I will add backlink?
Sincerely, Timur I. Alhimenkov
January 29th, 2009 at 2:24 am
XYX company allows you to write a check for $120 dated 18 days in the future payable to them; for which they give you $100 today. What’s the APR and EAR?
January 29th, 2009 at 8:36 pm
Whoah. XYX company must be Loan Shark Pte. Ltd. 20% for 18 days?!
Holding period return is 20%. EAR is (1 + 0.2)^(365/18) – 1 = 3930%. Is that what you’re looking for?
January 29th, 2009 at 8:39 pm
Hi Timur!
Yes, go ahead! Please let me know when it’s up
March 9th, 2009 at 11:11 am
Interesting way of doing the calculation. However, it is inefficient. Much more keystrokes.
4 keys compared to 9!
let’s say you had to change the decimal places even. Well that 4 more strokes right? [f] 4 to see four decimals and then [f] 2 to change back to default. even then it’s 8 to 9. I just leave my 12c on 4 decimals to begin with for the precision.
March 9th, 2009 at 10:49 pm
I do that too, actually (leaving 4 decimals in my HP12C).
Also Wolf, it’s not only the keystrokes, but also the “computation overhead” that’s happening in your head. With the method I detailed in this post, those are unnecessary. Just enter the numbers and you’re set.
June 21st, 2009 at 6:09 am
I’ve tried doing this following the steps exactly and I can’t seem to get it to run. When i put the 4 into n and then hit / then i, it merely puts 4 into i and nothing else. What am I doing wrong ???
June 22nd, 2009 at 9:23 pm
Hi MooNinja!
After you hit the / (that is, the divide button), you’re supposed to see 3 (12/4) there. So when you press i it will put 3 into i. Did you see 3 right after pressing /?