Three Ways a Loan Can Be Repaid
Not every loan works like a mortgage with equal monthly payments. Lenders and borrowers actually structure debt in three fundamentally different ways, and this calculator handles all three:
- Amortized Loan — fixed, equal payments made periodically until the balance hits zero. This is how nearly all mortgages, auto loans, personal loans, and student loans work.
- Deferred Payment Loan — nothing is paid until maturity, when the entire principal plus all accumulated interest comes due in one lump sum. Common for certain business loans and some deferred student loan structures.
- Bond — the reverse problem: given a fixed amount that will be paid out at a future date (the face value), what is that promise worth today? This is exactly how zero-coupon bonds are priced.
Switch between the three tabs above to model whichever situation applies to you — each uses its own formula, explained below.
Amortized Loan: The Formula Behind Your Payment
Every fixed-payment loan uses the same underlying math:
Payment = P × [ r(1 + r)n ] / [ (1 + r)n − 1 ]
Here P is the amount borrowed, r is the interest rate per payment period, and n is the total number of payments. Each payment splits between interest (what you owe the lender for borrowing the money) and principal (what actually reduces your balance) — early on, most of the payment is interest; by the final payment, it's almost entirely principal. That's why the amortization table above shows a shrinking "Interest" column and a growing "Principal" column as the schedule progresses.
Compound vs. Pay Back Frequency
Two separate settings control the math: how often interest compounds (accrues) and how often you actually pay. Most consumer loans compound and pay on the same schedule — monthly — but the calculator lets you set them independently, since some structured loans compound daily or annually while still collecting payments monthly.
Deferred Payment Loan: Growing Interest With No Payments
When nothing is paid until maturity, the balance simply compounds on itself:
Amount Due = P × (1 + r)n
Borrowing $100,000 at 6% annual interest with no payments for 10 years grows to roughly $179,085 — nearly 80% more than what was borrowed, entirely from compounding. This structure can be attractive when a borrower genuinely can't make payments during a startup or construction phase, but the total cost is almost always higher than an amortized loan at the same rate, since interest compounds on interest rather than shrinking against a falling balance.
Bond: Working Backward From a Future Payout
A bond calculation flips the deferred-payment formula around. Instead of asking "what will this loan grow into," it asks "what is a future payment worth right now":
Present Value = Face Value ÷ (1 + r)n
A bond promising $100,000 in 10 years, discounted at 6%, is worth about $55,839 today. This is the exact logic behind zero-coupon bonds and Treasury bills — the "interest" isn't paid out periodically, it's baked into the discount between what you pay now and what you collect later.
Interest Rate Types: APR, APY, and Why They Differ
An interest rate quoted as APR (Annual Percentage Rate) is a simple annual rate that doesn't account for compounding within the year. APY (Annual Percentage Yield) does — it reflects what you'd actually earn or owe after compounding is factored in. A 6% APR compounded monthly works out to roughly 6.17% APY. This calculator asks for a nominal annual rate and applies your chosen compounding frequency, matching how lenders actually calculate these numbers.
Choosing the Right Loan Term
A longer term almost always means a lower periodic payment but more total interest paid — the tradeoff isn't a fixed rule, it's a genuine judgment call based on cash flow needs versus long-term cost. Try the same loan amount at two different terms in the calculator above to see exactly how much a shorter term saves in interest versus how much it raises the payment.
Frequently Asked Questions
Why is my calculated payment slightly different from my lender's quote?
Small differences usually come from rounding conventions, day-count methods (30/360 vs actual/365), or fees folded into the lender's APR that aren't part of the base interest rate. For an exact match, confirm your lender's compounding and payment frequency match what you've entered here.
What's the real difference between an amortized loan and a deferred payment loan?
An amortized loan spreads both principal and interest across every payment, steadily reducing what you owe. A deferred loan collects nothing until the end, so interest compounds on the full balance the entire time — which is why the total cost is typically much higher for the same rate and term.
Can I use this for a car loan or personal loan, not just a mortgage?
Yes — the Amortized Loan tab works for any fixed-payment loan: auto loans, personal loans, student loans, and business term loans all use the identical formula, just with different typical rates and terms.
Does a shorter loan term always save money?
It saves on total interest almost every time, since you're borrowing the money for less time — but it raises the periodic payment, sometimes substantially. Whether that trade-off is worth it depends entirely on your monthly budget, not just the total interest figure.
How is a bond's present value affected by the discount rate?
A higher discount rate lowers the present value — the same $100,000 face value in 10 years is worth less today if you assume a higher rate, because money you could earn a high return on elsewhere is worth more in hand now than in the future.
This calculator is provided for educational and estimation purposes only and does not constitute financial advice. Actual loan terms, rates, and fees vary by lender — consult your loan agreement or a licensed financial professional for exact figures.