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Loan Amortization

3 formulas

Loan amortization formulas break down loan payments into their interest and principal components and track the remaining balance over time. These are critical for understanding mortgages, auto loans, and any installment debt — showing exactly how much of each payment goes toward interest versus reducing the balance.

Remaining Balance

Calculates the remaining loan balance after p payments have been made.

B=PV×(1+k)p−PMT×(1+k)p−1kB = PV \times (1+k)^p - PMT \times \frac{(1+k)^p - 1}{k}

Showing annual compounding

2 compounding options

Interest Portion of Payment

Calculates how much of a specific loan payment goes toward interest. Takes the original loan setup plus the payment number, computes the balance immediately before that payment, and multiplies by the per-period rate.

Interestp=Bp−1×km,Bp−1=PV(1+k/m)p−1−PMT⋅(1+k/m)p−1−1k/mInterest_p = B_{p-1} \times \frac{k}{m}, \quad B_{p-1} = PV(1 + k/m)^{p-1} - PMT \cdot \frac{(1 + k/m)^{p-1} - 1}{k/m}

Principal Portion of Payment

Calculates how much of a specific loan payment goes toward reducing the principal balance. Equals the total payment minus that payment's interest portion.

Principalp=PMT−Interestp=PMT−Bp−1×kmPrincipal_p = PMT - Interest_p = PMT - B_{p-1} \times \frac{k}{m}