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Unlike TI calculators, the HP 12c doesn't have or need a CPT button. It knows whether you've made a numeric entry or not. To calculate N, I, PV, FV, or PMT, simply press the appropriate key without entering a number.
I had the same problem with my HP 11C. The following solution worked for me.
1. Remove the battery cover.
2. With the batteries in place (i.e. DO NO REMOVE THEM), use a small piece of wire (I used a standard staple bent at one end), short the terminals FOR A BRIEF MOMENT between both ends of the set of batteries (the HP-11C has three). This means somehow inserting the staple such that the contacts in the batteries receptacle are shorted.
3. The flashing will stop. Then push the ON button until the calculator turns on. If it does not work the first time, remove the batteries and resinsert them.
4. You may have to repeat this procedure. I had to do it twice before my calculator worked again.
Check to see if the word "BEGIN" appears on your screen. If so, you are calculating the payment on an "annuity due" basis, that is, the first payment is made on day one, and each period thereafter, rather than the first payment being due at the end of the first (30 days usually) period. To fix this, press the blue "g" button, and then press the number "8" (notice the word "end" printed on that key in blue ink). This should return you to the normal (first payment due at the end of the period) option.