Payment Calculator

This calculator runs in two directions

Most loan calculators ask you the same three things and give you back one number. Amount, rate, term, and out comes the monthly payment. Useful, and also only half the story.

Because the question people actually have is usually the other one. Not "what will the payment be", but "I can afford about this much a month, so how long am I going to be doing this?"

The dropdown at the top switches between the two.

Same loan, same maths, entered from whichever end you actually know. If you are shopping and the lender has quoted you a term, use Fixed Term. If you are working backwards from your budget, use Fixed Payments.

The formula, and the same formula rearranged

When you know the term

This is the standard amortising loan payment, the one every bank uses for a fixed rate loan:

M = P × [ r(1 + r)ⁿ ] / [ (1 + r)ⁿ - 1 ]

So a 9 percent annual rate becomes 0.0075 a month, and a 5 year term becomes 60 payments.

When you know the payment

Now, if you already know M and want n instead, you rearrange the same equation and a logarithm falls out:

n = ln[ M / (M - P × r) ] / ln(1 + r)

The calculator then divides that by 12 and shows you the answer in years.

It is worth seeing that these are not two different formulas. It is one relationship between four quantities, and knowing any three gets you the fourth. The logarithm looks intimidating but it is only there because n is sitting up in an exponent and that is how you get it down.

One loan, run both ways

Lets take a 20,000 loan at 9 percent and put it through both modes, so you can see the two answers talking to each other.

Fixed Term: 5 years

The monthly rate is 9 divided by 12 divided by 100, which is 0.0075. The number of payments is 5 times 12, which is 60.

Fixed Payments: 500 a month

Same loan, same rate, but now we tell it we can manage 500 rather than the 415.17 the five year term asked for.

What that trade actually bought

Paying an extra 84.83 a month, which is 500 minus 415.17, finished the loan about twelve months early and saved 1,042.64 in interest.

That is the whole argument for paying more than the minimum, in two numbers. And it works the other way too. Drop to 400 a month on the same loan and the term stretches to 5.24 years, which is longer than the five year schedule you were originally offered.

Turning 3.98 years into something you can use

In Fixed Payments mode the answer arrives as a decimal number of years. 3.98 years. Nobody thinks in decimal years, so here is how to read it.

Multiply by 12. 3.98 times 12 is about 47.7 months, so call it 48 payments. That is the number you actually want, because loans are paid in whole months and your last one will be a slightly smaller odd amount rather than a full 500.

Two things follow from that. First, your real final payment will not match the tidy figure in the Total Payments row, because the calculator multiplies the payment by a fractional number of months rather than building a month by month schedule. Second, the gap is small. On the example above it is a few tens, not a few thousands.

If you want the month by month version with a payoff date attached, our repayment calculator builds the full schedule.

The payment that never finishes

Now the part that matters more than everything above it.

Every loan has a monthly payment below which you are not actually repaying anything. Work it out like this:

Monthly interest = Loan amount × annual rate ÷ 12 ÷ 100

On our 20,000 at 9 percent, that is 20,000 times 0.0075, which is exactly 150 a month.

Pay 150 and every rupee, dollar or peso goes to interest. The balance does not move. Not in year one, not in year forty. Pay 149 and the balance actually grows, because the interest you did not cover gets added to what you owe and then starts earning interest of its own. The Consumer Financial Protection Bureau calls this negative amortisation, and their description is blunt: if payments are less than the interest due each month, the balance will grow rather than decrease.

Try it in the calculator. Put in 20,000 at 9 percent and ask for a 150 monthly payment, and you get an error rather than an answer, because the maths has no solution. The loan genuinely never ends. Ask for 149 and you get an error too, for the same reason.

So before you talk yourself into the smallest payment a lender will accept, do that one multiplication. Whatever number comes out is the floor, and anything close to it means you are renting the debt rather than repaying it.

What the totals count, and what they do not

The Total Payments and Total Interest rows are built from the interest rate you typed in. That rate is the price of the money and nothing else.

Most loans also carry charges that sit outside it. Origination or processing fees, documentation charges, insurance the lender bundles in. Those are real money and they are not in the rate. The measure that does include them is the APR, and as the CFPB puts it, the APR is the interest rate plus the additional fees the lender charges, which is why it is usually the higher of the two numbers on your paperwork.

Which gives you a simple habit when comparing offers. Compare APR against APR, never APR against an interest rate. A lender quoting a lovely rate with a fat fee attached will look better than it is if you only read one of the two.

If the fee is an upfront percentage deducted from what you receive, our personal loan EMI calculator works out the effective APR once the fee is taken into account. And two more things worth knowing about what is on this page: the rate is treated as fixed for the whole term, so a floating rate loan will drift away from these numbers, and the monthly figure here is principal and interest only, with no property tax, insurance or escrow folded in.

One more time

Two modes, one relationship. Give it a term and it returns the payment. Give it a payment and it returns the term. Both come out of the same equation, just solved for a different unknown.

Paying more than the schedule demands shortens the term and cuts the interest, and the calculator will show you exactly how much of each. Paying less stretches it, and there is a floor below which the loan stops shrinking altogether. That floor is the loan amount times the annual rate divided by twelve hundred, and it is worth knowing before you sign anything.

And the totals here count interest only. Fees live in the APR, and the APR is the number to compare across lenders.

Hope that makes the two boxes a bit clearer. If something here does not match what your lender is telling you, do let us know, because we would rather find out we are wrong than have you working off a bad number.

Questions people ask

Which mode should I use?

Fixed Term when a lender has already quoted you a term and you want to know the damage. Fixed Payments when you know what your budget can absorb and want to know how long you will be carrying it.

Why do I get an error instead of an answer?

In Fixed Payments mode it usually means the payment you entered does not cover the monthly interest, so there is no term at which the loan finishes. Work out the loan amount times the annual rate divided by 12 and by 100, and enter something comfortably above it.

Does this work for a floating rate loan?

Only as a snapshot. It assumes the rate you typed holds for the whole term. On a floating rate loan the payment or the term will move whenever the rate resets, so treat the answer as what today's rate implies rather than as a schedule.

Can it show the effect of one extra payment?

Not directly, but you can get close. Run Fixed Payments with your regular amount, then run it again with the higher amount you think you can manage, and the difference in the two Total Interest figures is what the extra buys you.

Why does the result show a dollar sign?

The output is labelled in dollars, but the maths has no currency in it. Put in whatever you like and read the result in the same one. Percentages and ratios do not care.

What does 0.98 of a year mean in practice?

Multiply the decimal part by 12. 0.98 of a year is about 11.7 months, so a 3.98 year answer is roughly 48 monthly payments, with the last one smaller than the rest.

Does it handle fortnightly or weekly payments?

No, everything here is monthly. The rate is divided by 12 and the term is multiplied by 12, both of which assume twelve payments a year.

References

A note on the sources behind the two claims on this page that matter most. The description of what happens when a payment falls below the monthly interest, and the term for it, comes from the Consumer Financial Protection Bureau's own glossary rather than from us. The distinction between an interest rate and an APR, and the advice to compare like with like, is also the CFPB's, and it rests on the disclosure duties the Truth in Lending Act places on lenders.

1. Consumer Financial Protection Bureau, Mortgages key terms, on amortisation and negative amortisation. https://www.consumerfinance.gov/language/cfpb-in-english/mortgages-key-terms/
2. Consumer Financial Protection Bureau, What is the difference between a loan interest rate and the APR? https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-loan-interest-rate-and-the-apr-en-733/
3. Consumer Financial Protection Bureau, Auto loan answers: key terms, on how each payment splits between principal and finance charge. https://www.consumerfinance.gov/consumer-tools/auto-loans/answers/key-terms/
4. Cornell Law School, Legal Information Institute, Compound interest, Wex legal dictionary, on interest accruing on unpaid interest. https://www.law.cornell.edu/wex/compound_interest