What Is a Loan?
A loan is an agreement in which a lender gives money to a borrower, and the borrower agrees to return that money plus interest over an agreed period. The original sum is the principal; the charge for using it is the interest. Almost every loan in existence is a variation on one of three repayment structures, and this calculator covers all three.
The Three Loan Structures
1. Amortized loan — equal periodic payments
The most common structure. The borrower makes identical payments at regular intervals until the balance reaches zero. Each payment is split between interest, calculated on the current outstanding balance, and principal, which is whatever is left over. Because the balance falls with every payment, the interest portion shrinks and the principal portion grows over time. Mortgages, car loans, student loans and most personal loans work this way.
2. Deferred payment loan — one payment at maturity
Nothing is repaid until the end of the term, when the entire balance plus accumulated interest falls due in a single payment. Interest compounds on the full principal for the whole period, so the total cost is considerably higher than an amortized loan at the same rate. Short-term commercial borrowing and some student loan deferral periods use this structure.
3. Bond — a fixed amount due at maturity
Here the final amount is known and the question is what it is worth today. A zero-coupon bond with a $10,000 face value maturing in ten years is sold now for whatever sum, compounded at the market rate, grows to $10,000. This is the same arithmetic as a deferred payment loan, run backwards.
The Amortized Loan Formula
The periodic payment on an amortized loan is:
Payment = P × i ÷ (1 − (1 + i)−n)
where P is the principal, i is the interest rate per payment period, and n is the total number of payments. For a $25,000 loan at 7.5% over 5 years paid monthly, i = 0.075/12 = 0.00625 and n = 60, giving a payment of about $501.
Compounding vs. Payment Frequency
These are two separate settings and they are often confused. Compounding frequency is how often interest is added to the balance; payment frequency is how often you pay. When they differ, the stated annual rate must be converted into an equivalent rate for the payment period:
i = (1 + r ÷ c)c ÷ f − 1
where r is the annual rate, c is compounding periods per year and f is payments per year. The calculator does this automatically, which is why a loan quoted as 7.5% compounded daily costs slightly more than the same 7.5% compounded monthly.
Loan Payment Examples
All figures below assume a 7.5% annual rate with monthly compounding and monthly payments.
| Amount | Term | Monthly payment | Total repaid | Total interest |
|---|---|---|---|---|
| $5,000 | 3 years | $155.53 | $5,599.12 | $599.12 |
| $5,000 | 5 years | $100.19 | $6,011.38 | $1,011.38 |
| $10,000 | 3 years | $311.06 | $11,198.24 | $1,198.24 |
| $10,000 | 5 years | $200.38 | $12,022.77 | $2,022.77 |
| $25,000 | 3 years | $777.66 | $27,995.60 | $2,995.60 |
| $25,000 | 5 years | $500.95 | $30,056.92 | $5,056.92 |
| $50,000 | 3 years | $1,555.31 | $55,991.19 | $5,991.19 |
| $50,000 | 5 years | $1,001.90 | $60,113.85 | $10,113.85 |
How the Interest Rate Changes the Cost
A $20,000 loan over 5 years, at different annual rates:
| Rate | Monthly payment | Total interest |
|---|---|---|
| 4% | $368.33 | $2,099.83 |
| 6% | $386.66 | $3,199.36 |
| 8% | $405.53 | $4,331.67 |
| 10% | $424.94 | $5,496.45 |
| 12% | $444.89 | $6,693.34 |
| 15% | $475.80 | $8,547.92 |
| 20% | $529.88 | $11,792.66 |
The pattern is worth internalising: between 6% and 12% the monthly payment rises by roughly a fifth, but the total interest paid roughly doubles. Rate matters far more than the monthly payment suggests.
Secured and Unsecured Loans
| Secured | Unsecured | |
|---|---|---|
| Collateral | Required — the asset backs the loan | None |
| Interest rate | Lower | Higher |
| Typical amounts | Larger | Smaller |
| Risk to borrower | Loss of the asset on default | Credit damage, collections, possible lawsuit |
| Examples | Mortgage, auto loan, home equity loan | Credit card, personal loan, student loan |
Because the lender's downside is protected, secured loans are cheaper. That protection is the borrower's risk: missing payments on a mortgage or car loan can mean losing the house or the vehicle.
Interest Rate vs. APR
The interest rate is the cost of borrowing the money. The annual percentage rate (APR) adds the lender's fees — origination fees, discount points, some closing costs — and expresses the whole thing as a single annual figure. Two loans with identical interest rates can have quite different APRs, and APR is the number to compare when shopping between lenders. Note that APR assumes the loan runs to term; if you repay early, the effective cost of front-loaded fees is higher than the APR suggests.
What Determines the Rate You Are Offered
- Credit score — the single largest factor for consumer loans. The gap between excellent and fair credit is frequently 5 to 10 percentage points.
- Loan term — longer terms usually carry higher rates, because the lender is exposed for longer.
- Amount — very small and very large loans both tend to price higher than mid-range ones.
- Collateral — security lowers the rate substantially.
- Income and debt-to-income ratio — evidence that the payments are affordable.
- Prevailing market rates — consumer rates move with central bank policy rates, though not immediately or proportionally.
Frequently Asked Questions
Why does most of my early payment go to interest?
Interest is charged on the outstanding balance, which is at its highest at the start. As the balance falls, the interest portion of each fixed payment falls with it and more goes to principal. This is not a fee structure — it is simply arithmetic.
Does paying extra help?
Yes, and disproportionately so early in the term, because every extra dollar of principal removes all the future interest that dollar would have generated. Check first whether the loan carries a prepayment penalty.
Is a longer term cheaper?
The monthly payment is lower, the total cost is higher — usually much higher. Extending a loan from 3 to 5 years typically raises total interest by more than half.
What is the difference between this and the mortgage calculator?
The arithmetic of the amortized option is identical. The mortgage calculator adds property taxes, homeowners insurance, PMI and HOA fees, which apply only to property.