Annual Percentage Rate (APR) is the equivalent interest
rate of a loan including all loan fees and interests payed.
The monthly payment is calculated using following formula:
Where:
P: Monthly payment
C: Initial loan amount
E: All loan fees
r: Interest rate (%)
N: Pay terms
The total amount payed (T) is:
T = P * N + F
The total interest payed (I) is:
I = P * N - C - E
The direct-ratio APR formula is:
a = 6M * B/(3C(N+1) + B(N+1))
The constant-ratio formula is:
a = 2M * B /(C(N+1))
The N-ratio formula is:
a = M(95N + 9) * B/(12N(N+1)(4C + B))
Where:
a: APR
M: Number of payments per year
B: Total finance charges
F: Closing Fees
APR calculation Example:
A $300,000 loan with $4,000 other fees and an annual interest rate 5%, the payback term is 10 years.
The monthly payment = (300000 + 4000) * 0.05 * (1 + 0.05)120 / ((1 + 0.05)120 - 1) = 3224.39
The total payment = 3224.39 * 120 = 386927
The total interest = 386927 - 300000 = 86927
The Direct-ratio APR is 5.241%.
The Constant-ratio APR is 5.747%.
The N-ratio APR is 5.307%.
Note: The most frequently used method by the lender is the actuarial method, while the formula for which is
complicated due to the loan structure.
