How Fixed-Rate Loan Amortization Works
A standard fixed-rate loan requires equal periodic payments that gradually pay down both the accumulated financing interest and the underlying principal balance. Over the lifetime of the loan, the interest proportion of each monthly payment decreases as the remaining principal reduces.
The Standard Loan Payment Formula
The monthly payment $M$ on an amortizing loan is derived from the standard annuity formula:
$$M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}$$
Where:
- $P$: Loan principal balance (the amount borrowed)
- $r$: Periodic monthly interest rate ($\text{APR} \div 100 \div 12$)
- $n$: Total number of monthly installments ($\text{Years} \times 12$)
Handling 0% Interest Financing
When promotional financing offers $0\%$ APR ($r = 0$), the formula simplifies to standard linear division:
$$M = \frac{P}{n}$$
Practical Loan Calculation Example
Suppose you borrow $25,000 for an auto purchase at an annual interest rate of 6.5% over a 5-year term (60 months):
- Monthly rate $r = 0.065 / 12 = 0.0054167$
- Monthly payment $M = 25,000 \times \frac{0.0054167(1.0054167)^{60}}{(1.0054167)^{60} - 1} = \$489.15$
- Total of 60 payments $= \$489.15 \times 60 = \$29,349.00$
- Total interest paid over 5 years $= \$29,349.00 - \$25,000.00 = \$4,349.00$