OK, I'll give it a shot.
Since you purchased 200 points at $74 per point, your total charge should be $14,800.
You paid 10% up front, or $1480, leaving a principal balance of $13,320. Now, this differs from the $13,120 you stated, so we may have a either a typing error or you paid $200 down as well (maybe as an initial deposit?).
$13,320 would give us $111.00, and $13,120 would give us $109.33 for 120 principal payments.
The $7562.90 finance charge would also be spread over the 120 payments at $63.02 per month.
So, the total monthly payment would be either ($111.00+$63.02=$174.02) for a starting principal of $13,320 or ($109.33+63.02=$$172.36) for $13,120.
Plugging these into a simple interest loan calculator (which compounds yearly) yields an effective rate of 9.727% for the $13,320 amount, or 9.858% for the $13,120 amount.
So, they are both close to the 9.75% claimed. One is low by 0.02% and the other is high by 0.11%. The 9.727% is doubtful, seeing corporations almost never err in that direction. The 9.858% could possibly be explained by compounding errors.
If you're not familiar with this concept, consider a simple savings account. If you get 10% APR and it compounds yearly, you get your principal multiplied by 1.1. If, on the other hand, it's compounded monthly, you need to divide the yearly return by the number of compounding periods (in this case 12 months), add that to the principal and raise that number to the number of compounding periods. For 10% APR compounded monthly, the monthy return turns out to be 10%/12 = .0083333%. So, 1.00833333 to the 12th power (1.00833333^12) is 1.1047 or an effective yearly yield (APY) of 10.47% from the same 10% APR which gave us only 10% compounded yearly. For savings, that would work in our favor, for a loan, drum roll please.... you guessed it, it works against us.
Last, I haven't seen the math behind the online calculator I used (I am ashamed...), so things might just be wrong... sorry.
