How to Calculate Percentages, Tips, and Loan Amortization

Check percentage bases and split totals

A fall from 100 to 50 is a 50% loss, while returning from 50 to 100 requires a 100% gain. A rate moving from 5% to 7% rises by two percentage points and by 40% relative to its original rate.

For a 100.00 total split three ways, floor shares to 33.33 and allocate the remaining cent, producing 33.33, 33.33 and 33.34. Check the final sum and the intended tip base. Currency minor units vary; this two-decimal example is not a rule for every currency.

Use the contractual interest rate for amortization

For an equal-monthly-payment model, let P be principal, r the monthly contractual interest rate and n the payment count. For r > 0, M = P × r / (1 − (1 + r)^−n); for r = 0, M = P / n.

A 1,000 principal at a 12% nominal annual rate, monthly rate 1%, over 12 months gives an unrounded payment of about 88.8488. A real lender’s payment can differ because of rounding, payment dates or other terms. APR may include fees; it is not interchangeable with the nominal rate in this simple formula.

P = 1000
r = 0.12 / 12
n = 12
M = P * r / (1 - (1 + r) ** (-n))
// Approximately 88.8488 before payment rounding.

Reconcile the estimate with the actual terms

Check whether the agreement uses this equal-period model, how interest accrues, and which fees, taxes or escrow amounts are separate. Compare the estimate with the lender’s payment schedule and disclosures rather than labeling all of those differences arithmetic errors.

JavaScript Number uses binary floating-point arithmetic. It is not arbitrary-precision decimal money arithmetic, so displayed rounded amounts are estimates and intermediate rounding can matter. Keep bill splits in integer minor units where appropriate and reconcile the actual final total.

References

Use the linked specifications and product documentation to check behavior in your own environment.