What It Is:
APR is the interest rate that reflects all the costs of the loan, including fees, points, and other directly related costs. APR is not the same as Annual Percentage Yield (APY).
 
The oversimplified formula for APR is:
(Periodic interest rate) x (number of periods) = APR
 
In the real world, however, there are four methods to calculate APR: the actuarial method, the direct-ratio method, the constant-ratio method, and the N-ratio method. Lenders use the actuarial method most often, but it requires a computer to calculate because the formulas are very complicated and vary with the loan structure. Appendix J of Regulation Z in the Consumer Credit Protection Act provides the formulas, conditions, and examples of use of the actuarial method.
 
Visit
http://www.fdic.gov/regulations/laws/rules/6500-1950.html#6500appendixjtopart226
for the formulas behind the actuarial method.
 
The direct-ratio formula is:
APR = 6MC / [3P(N+1) + C(N+1)]     
Where:
M = number of payments per year
N = total number of payments
C = total finance charges
P = original loan proceeds
 
The constant-ratio formula is:
APR = 2MC / [P(N+1)]
 
The N-ratio formula is:
M(95N + 9)C / [12N(N+1)(4P+C)]
 
How It Works/Example:
Let’s assume XYZ Company borrows $1,000, which it must repay over 24 months. It has to pay $100 in closing costs to the lender. The nominal annual interest rate on the loan is 10%, compounded monthly. Below is the amortization schedule for this loan.

 
 
The APR under the direct-ratio method is:
APR = (6*12*$207.48) / [3*$1,000*(24+1) + $207.48(24+1)] = $14,938.56 / $80,187 = 18.63%
 
The direct-ratio method tends to understate the actual APR. Note that the APR in this example is considerably higher than the 10% nominal interest rate used to calculate the payments. This is because the APR incorporates the closing costs, which are part of the cost of borrowing this money.
 
The APR under the constant-ratio method is:
APR = (2*12*$207.48) / [$1,000*(24+1)] = $4,979.52 / $25,000 = 19.92%
The constant-ratio method tends to overestimate the actual APR.
 
The APR under the N-ratio method is:
APR = [12*(95*24+9)*$207.48] / [12*24(24+1)(4*$1,000 + $207.48)] = $5,699,060.64 / $30,293,856 = 18.812%
The N-ratio method tends to give an APR closer to the “real” (actuarial method) APR.
  
Why It Matters:
Lenders offer a multitude of interest-rate structures, fees, private mortgage insurance, and points. Knowing a loan’s APR tells the borrower what the true cost of borrowing is because it includes all of the fees directly related to the loan, not just the interest payments.
 
The onus of calculating APRs is on the lender, not the borrower. Federal regulations require lenders to disclose a loan’s APR in large type, and the Consumer  Credit Protection Act of 1968 (also known as the Truth in Lending Act) requires lenders to disclose a loan’s finance charges and its APR so that borrowers can meaningfully compare loans.
 
However, the fact that there is more than one way to calculate an APR complicates the task of comparing APRs. Additionally, APR calculations are based on fixed interest rates; adjustable rates carry ever-changing APRs. Further, it is important that a borrower compare loans with identical maturities. A shorter loan could have a lower interest rate but a higher APR, because the loan fees amortize over a shorter period of time. For these reasons, some borrowers turn to good faith estimates from lenders to compare loan fees directly rather than compare the APRs.
 

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