FINANCIAL CALCULATION GUIDE
How Loan Payments Are Calculated
Learn how fixed monthly installment payments are derived, how periodic monthly interest is calculated, and how compounding influences borrowing costs.
Amortization Formula
The mathematical equation lenders use to establish fixed monthly installments.
Periodic Interest Rate
How annual nominal interest rates are converted to monthly rates (r = Rate ÷ 12).
Worked Numbers
Step-by-step substitution demonstrating exactly where your monthly dollar amount comes from.
1. The Fixed-Rate Amortization Formula
When borrowing money under a fixed-rate installment plan, lenders compute your regular payment using the annuity formula:
M = P × [ r(1 + r)^n ] ÷ [ (1 + r)^n − 1 ]
Where:
- • M: Total monthly payment
- • P: Principal loan balance
- • r: Monthly periodic interest rate (Nominal Annual Rate ÷ 1200)
- • n: Total term length in months (Years × 12)
2. Worked Calculation Example
Suppose you borrow $10,000 at an annual nominal rate of 6% for 5 years (60 months):
- 1. Monthly rate r = 0.06 ÷ 12 = 0.005
- 2. Factor (1 + r)^60 = (1.005)^60 ≈ 1.34885
- 3. Numerator = 10,000 × 0.005 × 1.34885 ≈ 67.4425
- 4. Denominator = 1.34885 − 1 ≈ 0.34885
- 5. Monthly Payment M = 67.4425 ÷ 0.34885 = $193.33
3. Interactive Loan Calculator
Calculate your exact monthly payments and generate an interactive amortization schedule:
Frequently Asked Questions
What is the standard amortization equation?
The formula is M = P × [r(1 + r)^n] ÷ [(1 + r)^n − 1], where M is monthly payment, P is the principal amount borrowed, r is the monthly interest rate (Annual Rate ÷ 100 ÷ 12), and n is the total number of monthly payments.
Does this formula apply to mortgages and car loans?
Yes. Any fully amortizing, fixed-rate installment loan with regular monthly payments uses this exact mathematical formula.
Why does multiplying the monthly payment by term length exceed the borrowed amount?
The difference between total payments and original principal represents total interest paid to the lender for borrowing the capital over time.