How to calculate the monthly interest rate on a loan

[Dahu]

We've been offered a loan, fixed for the next 10 years.

Annual interest rate quoted is 4.6%.

Payments to be made monthly.

So what is the standard way of calculating the monthly interest rate to be applied? Is it simply 0.046/12 = 0.3833%?

Or should it be (1.046)^(1/12) -1 = 0.3755%?

The bank has calculated the repayments based on the first method, is this standard in the industry? I would have though the second method would be more correct.

[dracoi]

APR does not take compounding into account. It's the number that's required to be disclosed by law and is presumably better than the rules that existed previously, but you're right - an APR of 4.6% is not 4.6% per year when you compound it. Credit cards use daily compounding on a daily average balance, so the compounded interest and the APR are event farther apart there.

On the other hand, if you make monthly payments, the interest isn't compounding because you pay it off each month.

[Gfactor]

This doesn't respond directly to the OP, but here is a good discussion of some issues with APR: http://www.mtgprofessor.com/tutorial_on_annual_percentage_rate_(apr).htm

Here is a discussion of mortgage amortization calculations: http://www.mtgprofessor.com/A%20-%20Amortization/how_do_amortized_mortgages_work.htm

And a more math-oriented one: http://www.hughchou.org/calc/formula.html

Even more math fun: http://www.ruralfinance.org/servlet/BinaryDownloaderServlet?filename=1133308852080_Lesson_4_interest_rates.pdf