The standard amortization formula is: M = P × [r(1+r)n] ÷ [(1+r)n - 1], where M is the monthly payment, P is the principal, r is the monthly interest rate, and n is the number of payment periods. The monthly rate r is the annual percentage rate divided by {{SLOT:months_per_year}}. The term (1+r)n is called the growth factor — it represents how the balance would grow if no payments were made.
Working through the example: with a principal of {{SLOT:example_principal}} dollars, an annual rate of {{SLOT:example_rate}} percent, and a term of {{SLOT:example_term}} months, the monthly rate is the annual rate divided by {{SLOT:months_per_year}} times one hundred. The growth factor is one plus that monthly rate, raised to the power of {{SLOT:example_term}}. Multiply the principal by the monthly rate and the growth factor, then divide by the growth factor minus one. The result is the monthly payment of {{SLOT:monthly_payment}}.
When the interest rate is zero, the formula breaks down mathematically because the denominator becomes zero. In that case the payment is simply the principal divided by the number of months — a plain equal-share split. Total interest is always the monthly payment multiplied by the number of months, minus the original principal. Interest as a percentage of the loan is total interest divided by principal, converted to a percentage. These downstream figures are exact given the inputs — no rounding is applied until the final display step.
## What you put in ## What comes out - **Monthly Payment** ## A worked example This spec carries no worked example. ## When the answer changes - Loan amount is below 500 dollars. Most personal loan minimums start around 1,000 dollars. Results may not reflect real offers. (principal < 500) - Loan amount exceeds 100,000 dollars. Personal loans above this level are uncommon. Consider whether a home equity or business loan is more appropriate. (principal > 100000) - Annual rate exceeds 36 percent. This is above the threshold many consumer advocates consider the ceiling for affordable lending. Verify the rate on your offer document. (rate > 36) - Loan term is under 6 months. Very short terms are unusual for personal loans and produce very high monthly payments. Confirm the term length with your lender. (term < 6) - Loan term exceeds 84 months. Most personal loans are capped at 84 months. Check whether your lender actually offers this length. (term > 84) --- source: sha256:0a59fffc5e6618f9eac824036c886fa84559cf2a6a4a62578f50d3ebe3ba88a0