Loan Calculator

Formula

PMT = P × i / (1 − (1+i)^−n), where i = periodic rate from EAR, n = total payments. EAR = (1+r/m)^m − 1.

Deferred lump sum: Due = P×(1+r/m)^(m×t). Zero-coupon bond price: Price = Face ÷ (1+r/m)^(m×t).

How it works

Pick amortized, deferred, or bond mode. For amortized loans the engine converts your nominal APR and compounding frequency into an effective annual rate, then into a per-payment periodic rate, then solves the level-payment formula. Deferred mode grows principal with compound interest to a single due amount. Bond mode discounts a face value back to today’s price at the same growth factor.

Assumptions

• Level payments at regular intervals; no skipped or graduated payments.
• Nominal APR with discrete compounding (or continuous via e^rt); fees excluded from APR.
• Extra payments apply fully to principal in the period paid.

Default result

With Defaults: $10,000 amortized, 5 years, 6% APR, monthly compounding and payments: Payment $193.33/mo × 60 = $11,599.68 total · interest $1,599.68

Worked examples

Auto-style amortized loan

$10,000 loan, 5 years, 6% APR, monthly compounding, monthly payments

$193.33/mo for 60 months · total $11,599.68 (interest $1,599.68) — Example calculated with this calculator's formula.

Deferred single payment

$10,000 principal, 5 years, 6% APR, annual compounding, paid once at maturity

Due at maturity $13,382.26 (interest $3,382.26 on $10,000) — Example calculated with this calculator's formula.

Frequently asked questions

How is a loan monthly payment calculated?

For an amortized loan, the payment is calculated with the formula P = A x i / (1 - (1 + i)^-n), where A is the loan amount, i is the periodic interest rate, and n is the total number of payments. The periodic rate is derived from the annual rate and the selected compounding frequency.

What is the difference between APR and APY?

APR (annual percentage rate) is the nominal yearly interest rate including fees, while APY (annual percentage yield) reflects the effect of compounding over a year. For the same nominal rate, more frequent compounding produces a higher APY.

What is a deferred payment loan?

A deferred payment loan requires a single lump-sum payment of all principal and accrued interest at maturity rather than periodic installments. Interest still compounds over the term, so the amount due grows the longer repayment is deferred.

What is a zero-coupon bond?

A zero-coupon bond pays no periodic interest. Instead, it is sold at a discount to its face value, and the investor receives the full face value at maturity. The Bond calculation above solves for the discounted price given a predetermined due amount.