Annual Percentage Rate (APR)
Annual Percentage Rate is the total cost of credit expressed as a yearly percentage rate. In broader terms, APR is the function or the combination of the principal loan amount, additional loan costs, rate of interest and the duration of the loan. Interest and other charges added together form the APR.
Fees to be added while calculating the APR:
- Discount fees and origination fees.
- Pre-paid interest fees.
- Loan processing fees.
- Underwriting fees.
- Document preparation fees.
- Private mortgage insurance.
Symbolical Denotation: APR = f (P, I, A, N) where,
P = principal loan amount,
A = additional cost,
I = interest rate,
N= number of months.
From the above equation, it can be derived that the value of APR which is an independent variable depends on the value of the principal loan amount, the rate of interest the additional cost, and the number of months which are all dependent variable.
Example:
Suppose, Loan amount (P) = $100.
Additional cost (A) = $10 Interest rate (I) = 10%, monthly interest rate = R/100*12 =0.008(10/100*12) Number of months = 1 month.
Hence monthly payment required is:
Monthly payment (M) = (P+A) r(1+r)n / (1+r)n-1 Putting the above data in the equation we get, M = (100+10)0.008(1+0.008)1/ (1+0.008)1-1
= (110) 0.008 (1.008)
= (1.008)-1
= 0.88704
= 0.008
= 110.88
Hence the monthly payment which is required is 110.88. The annual percentage rate will now be found out by the application of
Newton Raphson Method. The equation of Newton Raphson Method is -
[a (1+a)n/ (1+a)n-1]- P/C = 0
Putting the value of the monthly payment in the equation and solving for 'a': [a (1+a)1/ (1+a)1-1]- 110.88/100 = 0, After solving the equation: a = 130.56 %
So from the above calculation it can be concluded that if you take a loan of $100, having additional cost of $10 and interest rate of 10% then its APR will be 130.56 %. If there had been no additional cost then APR and interest rate would have been equal.
