Hello, can you please help me with this question?

"A interest rate manipulator offers you the following: If you borrow $1,000 for three years at 17.3% interest, in three years you owe him 1000*(1+17.3%)^3 = $1,613.96. The manipulator has decided to break down the payments for you per month and accordingly allows you to make low monthly payments of 1,613/36 = $44.83 per month, as a favor". Is the interest rate on this loan really 17.3%? Why or why not? What is the APR on this loan? What is the EAR? Why is it called add on interest?

Okay let me take a step back to what I know.

• (FV/PV)^(1/n) - 1 => effectively how much interest we are paying on the loan, doing this I get 17.3% so I do not see anything weird about this loan.
• Treating this as a PV annuity and solving for r I get
• PV = 1000
• Pmt = -44.83 <-if I pay him $44.83 every month for 36 months, I am still ending up paying $1,613 the loan amount .. why is it ok to pay the $1,713 at the end of the third year but not split it?
• N = 36
• CPT I/Y -> 2.856% per month