NO, the APR will not change your payments, the payments are based on the note rate of 4.625%. The Annual Percentage Rate (APR) is the cost of your credit expressed as an annual rate. Because you may be paying loan discount â€˜pointsâ€™ and other â€˜prepaidâ€™ finance charges at closing, the APR disclosed is often higher than the interest rate on your loan. This APR can be compared to the APR on other loan programs to give you a consistent means of comparing rates and programs. At least that is what is "supposed" to happen, but since what a lender chooses to disclose in the APR calculation is somewhat "fuzzy" it tends to just confuse matters.
The APR in your case is a little high but not that terrible. The spread between the note rate (4.625%) and the APR (5.6%) on an FHA mortgage is much greater than on a conventional mortgage because of the mortgage insurance. I just ran the numbers based on todays rates using a 620 credit score, usual closing costs and assuming the broker /lender was making around $5000, I get an APR of 5.538%. I have heard NY has other fees that I may not be including so your APR may very well be right on target.
Hope that helps.