The math behind loan amortization
The monthly payment for an amortizing loan is calculated using the formula: M = P × [r(1+r)^n] / [(1+r)^n - 1], where P is the principal, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of payments (loan term in years × 12). This formula ensures each payment covers the interest accrued since the last payment and the remainder reduces the principal. Over the loan term, the interest portion decreases and the principal portion increases — a process called amortization.
Our calculator generates a full amortization schedule showing the principal/interest breakdown for every payment. This is critical for understanding the total cost of borrowing: a 30-year mortgage at 6% APR costs almost as much in interest as the principal itself. The schedule also shows the remaining balance after each payment, useful for calculating the cost of early repayment or refinancing.
Loan comparison: fixed vs variable rate
Fixed-rate loans lock in the interest rate for the entire term, providing predictable payments. Variable-rate loans (ARMs) have lower initial rates that adjust periodically based on an index (like SOFR) plus a margin. Our calculator supports ARM scenarios by letting you set an initial rate, adjustment period, and maximum rate cap. Run scenarios with the maximum possible rate to stress-test your budget — if the fully indexed rate would break your finances, a fixed-rate loan may be safer.
Our calculator also handles interest-only loans (where payments cover only interest for the first N years, then switch to fully amortizing payments). This is common for commercial real estate and construction loans but risky for personal mortgages because no equity is built during the interest-only period.