Sean B wrote:
No, APR is different than interest rate, it takes into account the costs
associated with the loan and adds that to the actual interest charged during
the life of the loan. Then it backs into what the interst rate is given those
costs + interest rate = APR.

That is correct. So I presume you want to know how to compute the US
"Truth in Lending" APR. Right?

With respect to US mortgages, "APR" is a technical term defined in
Regulation Z and Appendix J. It should not be confused with the
(nominal) annual interest rate.

There seems to be two common ways to compute APR, exhibited by the
following online calculators:
http://www.mortgageloan.com/calculators/aprcalc.cgi [1] and
http://www.lendingtree.com/cec/tools...ortgageAPR.asp [2].

For the first method, the actual payment is determined based on the
actual loan amount. Then an effective monthly rate is computed based
on the actual loan amount minus the applicable closing costs, which is
then multiplied by 12 per US regulation. In your example, the APR
would be:

=12 * rate(12*30, pmt(7%/12, 12*30, -100000), -100000+2000)

The result of the formula (7.2014%) matches the result of the
mortgageloan.com calculator.

For the second method, a fictious payment is determined based on the
actual loan amount plus the applicable closing costs. Then an
effective monthly rate is computed based on the actual loan amount,
which is again multiplied by 12. Note that this fictious payment is
solely for the purpose of computing an APR; it is not the actual
payment. In your example, the APR would be:

=12 * rate(12*30, pmt(7%/12, 12*30, -100000-2000), -100000)

The result of that formula (7.1973%) matches the result of the
lendingtree.com calculator.

Despite the apparent difference in the results of the two methods, note
that in this case at least, they are the same when rounded to a basis
point (1/100 of a percent), which is well within the accuracy
requirements of the federal regulations. I have not examined the
underlying math formulas to see if perhaps the two methods are in fact
identical mathematically.

Having said all that, it should be noted that despite attempts by
federal law to create a standardized "rate" to use when comparing loan
offerings, the fact is: the APR is virtually useless, IMHO. The main
reason is that different lenders include different fees in what I
called "applicable closing costs". Federal regulations specify only a
minimum set. More importantly, federal regulations permit the
exclusion of many fees that are highly variable among lenders. As a
consequence, the APR fails to give a truly comparable value of the cost
of lending. Refer to http://www.mtg-net.com/sfaq/faq/apr.htm for
details.

Bottom line: Other than as an academic exercise, ignore the APR.


-----
[1] At one time, I found an online explanation of the first APR method,
exhibited by http://www.mortgageloan.com/calculators/aprcalc.cgi .
But, sigh, I cannot find that link again.

[2] An explanation of the second APR method, exhibited by
http://www.lendingtree.com/cec/tools...ortgageAPR.asp , can
be found by clicking View Report on that web page.