Your friend wants to borrow $1,137.45 from you to pay off a credit card that charges a 14.7% apr. you agree to the loan but require your friend to pay you interest of 3.6% apr on the loan and your friend agrees. your friend pays you $200.00 at the end of the first month. how much goes toward the principal?

$196.59  
Let's start by calculating the interest on the first month. 1137.45 * (0.036/12) = 1137.45 * 0.003 = 3.41235 
 So at the end of the 1st month, the amount owed will be 1137.45 + 3.41 = 1140.86 
 And after the 200 payment is done, the new balance will be:
 1140.86 - 200 = 940.86 
 Meaning that the principle reduced is: 1137.45 - 940.86 = 196.59 
 We could have also gotten the amount going towards the principle by subtracting the interest from the paying like: 200 - 3.41 = 196.59