Personal Loan Calculator

A personal loan is unsecured installment debt repaid in equal monthly amounts, and the payment formula M = P r (1+r)^n / ((1+r)^n - 1) is the algebraic solution to setting the present value of n level payments, discounted at the monthly rate r, equal to the principal P. Because each payment is identical while the outstanding balance shrinks, the interest share of every payment falls and the principal share rises across the term. The apparent front-loading of interest is a consequence of that arithmetic rather than a lender choice: on a 15,000 dollar loan at 9.5 percent over 36 months the payment is about 480 dollars, of which the first month is 118.75 dollars interest and roughly 362 dollars principal, while the last payment is almost entirely principal. The stated interest rate is not the cost of the loan whenever an origination fee applies. Fees of 1 to 8 percent are deducted from the disbursement, so the borrower receives less than the amount being amortized while repaying the full figure, and the true cost is the internal rate of return that equates the payment stream to the cash actually received. That is the number the Truth in Lending Act requires lenders to disclose as the APR, and it is what this tool solves for numerically. Unsecured personal loan APRs commonly range from about 6 percent for excellent credit to 36 percent, the ceiling many lenders observe voluntarily and the cap the Military Lending Act imposes for covered service members.

The mathematics long predates the consumer product. Level-payment annuity valuation was worked out in early modern Europe for loans and life contingencies: Richard Witt published compound interest tables in London in 1613, and Edmond Halley applied present-value reasoning to annuities in 1693 using mortality records from Breslau. Applying that arithmetic to small unsecured borrowing came much later. Arthur J. Morris opened a bank in Norfolk, Virginia in 1910 that lent modest sums to wage earners against character references and co-signers rather than collateral, repaid in regular installments, and the Morris Plan model spread across the country. In 1916 the Russell Sage Foundation promoted a Uniform Small Loan Law that legalized such lending at regulated rates and drew borrowers away from unlicensed lenders. Disclosure arrived last. Before 1968 lenders quoted charges in mutually incompatible ways, including add-on and discount methods that made the effective rate very hard to see, so two offers could not be compared directly. The Truth in Lending Act, passed that year as Title I of the Consumer Credit Protection Act and implemented through the Federal Reserve's Regulation Z in 1969, required a single annual percentage rate computed to include finance charges such as origination fees. Online marketplace lenders that emerged after 2006 competed largely on that disclosed number, and supervision of the disclosures moved to the Consumer Financial Protection Bureau, created by the Dodd-Frank Act in 2010.