Loan calculator
Work out the payment on a loan, what it costs in interest and fees, and when it is paid off — or what a loan repaid in one sum, or a bond, comes to.
Monthly payment
$469.57
Principal and interest on $10,000.00 at 11.75%, paid monthly over 2 years.
- Total interest
- $1,269.63
- Number of payments
- 24
- Total of payments
- $11,269.63
- Paid off
- —
What you pay
- Principal$10,000.00
- Interest$1,269.63
- Principal each year
- Interest each year
| Year | Total payment | Interest | Principal | Balance |
|---|---|---|---|---|
| Year 1 | $5,634.82 | $926.81 | $4,708.01 | $5,291.99 |
| Year 2 | $5,634.82 | $342.83 | $5,291.99 | $0.00 |
Three ways to borrow, three calculations
You repay an amortized loan in equal payments. Each payment first covers the interest on the balance for that period, and the rest repays part of the loan, so the balance reaches zero with the last payment. The payment is loan amount × i ÷ (1 − (1 + i)^−n), where i is the interest rate for one payment period and n is the number of payments; at 0% it is the loan amount ÷ n. The total interest is the sum of the payments minus the loan amount.
A deferred-payment loan has no payments until the end of the term, when you repay the amount borrowed and all the interest in one sum. Interest is added to the balance each compounding period and then earns interest itself, so the amount due is loan amount × (1 + r ÷ m)^(m × t), where r is the yearly rate, m the number of compounding periods a year and t the term in years. The total interest is the amount due minus the amount borrowed.
A zero-coupon bond pays no interest along the way: it costs less than its face value today and repays the face value at maturity. The calculator works back from the amount due: value today = amount due ÷ (1 + r ÷ m)^(m × t). The difference, often called the discount, is the interest. The effective yield, (1 + r ÷ m)^m − 1, is the yearly rate with compounding included.
Compounding and payment frequency
The rate you enter is a yearly nominal rate, and the calculator turns it into a rate for one payment period. When interest compounds as often as you pay, the default for an amortized loan, that rate is the yearly rate ÷ the number of payments a year: 11.75% ÷ 12 for monthly payments.
When interest compounds at another frequency, the rate for one payment period is (1 + r ÷ m)^(m ÷ q) − 1, where r is the yearly rate, m the number of times interest compounds a year and q the number of payments a year. Compounding more often than you pay makes each payment slightly larger, and compounding less often makes it slightly smaller.
A year counts as 12 months, 24 half-months, 26 periods of two weeks, 52 weeks or 365 days. Deferred-payment loans and bonds have no regular payments; their interest compounds yearly unless you choose another frequency.
Interest rate and true cost
The interest rate on your offer, also called the nominal rate, is what the payments are worked out from. Lenders often add fees, such as an arrangement or origination fee, which raise the cost of the loan without changing that rate. So that offers can be compared, lenders in most countries must also show a yearly rate that includes the fees.
Its name differs by country: the APR in the United States, Canada and the UK; the APRC in the European Union and Iceland, usually under a local name such as TAEG or effektiver Jahreszins; the effective rate in Switzerland and Norway; the comparison rate in Australia; and the effective interest rate (EIR) in Singapore. New Zealand law defines no such rate.
To work it out, the calculator finds the rate per payment period at which your payments are worth exactly what you receive: the loan amount minus any fees paid up front. A fee added to the loan raises the payments but not what you receive. That rate becomes a yearly one in one of two ways. The nominal way multiplies it by the number of payments a year, as in the United States and Australia, and here for New Zealand and Singapore, where no law sets a method. The effective way compounds it, (1 + rate per period)^(payments a year) − 1, as in the European Union, the UK, Switzerland, Norway and Iceland. The note for your country below says which applies. Canada’s APR uses a formula of its own, described in its note.
With more than one payment a year, an effective rate is above the interest rate even without fees: 7.25% paid monthly is 7.50% as an effective rate. The calculator shows the rate only when you add fees.
Which fees count differs by country. US rules leave out application fees that every applicant pays, EU rules leave out notary fees, and Australian rules leave out government fees and charges. The calculator counts every fee you enter.
In the United States, Regulation Z (12 CFR 1026.22 and Appendix J) defines the APR as the rate per payment × the number of payments a year. It counts fees such as points and loan fees, but not application fees that every applicant pays, or late charges.
| Country | Name | Defined in |
|---|---|---|
| Australia | Comparison rate | National Credit Code |
| Austria | APRC (effektiver Jahreszins) | Verbraucherkreditgesetz (VKrG, § 27) |
| Belgium | APRC (JKP / TAEG) | Code of Economic Law (article I.9, 42°) |
| Canada | APR | Financial Consumer Protection Framework Regulations |
| Denmark | APRC (ÅOP) | Credit Agreements Act (kreditaftaleloven, § 16 and Annex 1) |
| Finland | APRC (todellinen vuosikorko) | Consumer Protection Act (kuluttajansuojalaki, chapter 7) |
| France | APRC (TAEG) | Code de la consommation (articles L314-1 to L314-5) |
| Germany | APRC (effektiver Jahreszins) | Preisangabenverordnung (PAngV, § 16) |
| Iceland | APRC (ÁHK) | Consumer credit law no. 33/2013 (article 21) |
| Ireland | APRC | S.I. No. 281/2010 |
| Italy | APRC (TAEG) | Testo unico bancario (article 121) |
| Luxembourg | APRC (TAEG) | Code de la consommation (articles L. 224-2 and L. 224-20) |
| Netherlands | APRC (JKP) | Burgerlijk Wetboek (book 7, articles 57 and 71) |
| New Zealand | Rate including fees | None: lenders list the annual interest rate and each fee (Credit Contracts and Consumer Finance Act 2003) |
| Norway | Effective rate (effektiv rente) | Financial Contracts Act (finansavtaleloven, § 1-7) and its regulation |
| Singapore | EIR (effective interest rate) | No law; the Association of Banks in Singapore’s Code of Banking Practice |
| Spain | APRC (TAE) | Ley 16/2011 (article 32 and Annex I) |
| Sweden | APRC (effektiv ränta) | Consumer Credit Act (konsumentkreditlagen) |
| Switzerland | Effective annual rate (effektiver Jahreszins) | Consumer Credit Act (KKG, articles 33 and 34 and Annex 1) |
| United Kingdom | APR | FCA consumer credit rules (CONC App 1.2) |
| United States | APR | Regulation Z (12 CFR 1026.22 and Appendix J) |
Formula sources: the Wikipedia articles Amortization calculator (payment), Compound interest (compounding and converting between frequencies), Present value (bond value) and Effective interest rate (effective yield). Each country’s rate that includes fees follows the law named in its note.
Frequently asked questions
Is this the same as an EMI calculator?
Yes, for a loan repaid in equal monthly payments. EMI, short for equated monthly installment, is the name used in India for that payment. With the default settings, an amortized loan with monthly payments, enter the loan amount, the yearly interest rate and the term: the payment shown is the EMI, from the same formula. India is not in the country list, so amounts show another currency; the figures are the same.
How is the monthly payment on a loan calculated?
The payment is loan amount × i ÷ (1 − (1 + i)^−n), where i is the interest rate for one month and n the number of monthly payments. When interest compounds monthly, i is the yearly rate ÷ 12. For example, $10,000 at 11.75% over 2 years gives i of about 0.98% and n = 24, so the payment is $469.57 a month.
How much interest will I pay on a loan?
The total interest is all your payments added up, minus the amount you borrowed. In the example above, the 24 payments add up to $11,269.63, so the interest is $1,269.63. Each payment’s interest is the monthly rate × the balance still owed, so it is highest at the start, $97.92 in the first month, and falls to $4.55 in the last. The schedule shows the split for every payment or year.
Which rate do I enter: the interest rate or the APR?
Enter the yearly interest rate on your offer, also called the nominal rate. The APR, and similar rates such as the APRC in Europe or the comparison rate in Australia, already include fees, so entering one as the interest rate overstates the payment. To see the rate that includes fees, open Fees and enter them: with a 5% origination fee paid up front, $10,000 at 11.75% over 2 years has an APR of 16.97%.
How does a longer loan term change the cost?
A longer term lowers each payment but adds interest, because the balance is repaid more slowly. $10,000 at 11.75% costs $469.57 a month over 2 years, with $1,269.63 in interest; over 5 years the payment falls to $221.18 and the interest rises to $3,270.99.
Does it matter how often interest compounds?
A little. When interest compounds more often than you pay, each payment is slightly higher; when it compounds less often, slightly lower. For $10,000 at 11.75% over 2 years with monthly payments, the payment is $469.57 with monthly compounding, $469.83 with daily compounding and $466.83 with yearly compounding.
Does it work for personal, car and bank loans?
Yes, for any loan with a fixed interest rate repaid in equal payments, secured or not: personal loans, car loans and bank loans. It does not cover a rate that changes during the loan, extra payments or a final balloon payment.
Can I use this loan calculator outside the US?
Yes. It covers 21 countries in North America, Europe and the Asia-Pacific region; the Country field lists them all. The country sets the currency, the number format, the example values and the local name and method of the yearly rate that includes fees. The payment is worked out the same way in every country.