Loan payment
v1capitalinteresmesescuota_mensualHow it is worked out
Work out the fixed monthly payment on a loan from the amount borrowed, the annual interest and the term in months.
The payment comes from an amortising loan: every instalment is the same, and each one covers the interest on what is still owed and puts the rest towards the principal. The annual rate is divided by twelve to make it monthly, and the term enters as a negative exponent because it discounts to today what will be paid in the future.
The expression that runs
capital * (interes / 100 / 12) / (1 - (1 + interes / 100 / 12) ^ -meses)The fields arrive with an example filled in: put your own numbers in and run it again. You can also edit the formula to fit your case.
What if the formula were yours?
This calculator is not hand-written: it is an Axioma formula. Open it in the editor to see how it is built, adapt it to your case and create the ones you need.
How each payment is made up
On 30 million at 18 % a year over 60 months, the payment is 761,803 and does not change for five years. What changes is what is inside it: 18 % a year is 1.5 % a month, so in the first month 450,000 goes to interest on the outstanding balance and only 311,803 reduces the debt. By the last month it is almost all capital.
That is why paying extra towards capital pays off so much: what you bring forward erases the payments at the end, the ones carrying the least interest, and with them all the interest that would have accrued until then. Over the full 60 payments you hand over 45.7 million, of which 15.7 is interest.
Which rate to type in
The field asks for the nominal annual rate, the one divided by twelve to get the monthly rate. Many lenders quote an effective annual rate instead, and the two are not the same: an effective 18 % is a monthly 1.3888 %, which is a nominal annual rate of 16.67 %.
If your rate is quoted as effective, convert it first: raise 1.18 to the power of one twelfth, subtract one and multiply by twelve. Typing an effective annual rate as if it were nominal inflates the payment, and it is the usual reason this number does not match the one the lender gave you.
What the payment does not include
The formula returns the financing payment: capital plus interest. On top of it lenders usually add life or unemployment insurance, origination fees and account charges, which on consumer loans can add a far from negligible share of the monthly outlay.
That is why comparing two loans by the payment alone leads to picking the longest term, which is always the most expensive. What is worth comparing is the total handed over by the end, and how much of that total is interest.
Frequently asked questions
- Why does my lender quote a different payment?
- Usually the rate: if you were quoted an effective annual rate and typed it here as nominal, the payment comes out higher. After that come insurance and account fees, which the lender adds to the payment and this formula does not.
- How much do I save by paying extra towards capital?
- What you save is the interest that will now never accrue. Paying extra reduces the balance the monthly 1.5 % is charged on, so the effect is larger the earlier you do it and the longer the remaining term.
- Should I take a longer term so the payment drops?
- The payment drops and the cost rises. The same 30 million at 18 % over 84 months gives a payment of around 630,000, but interest goes from 15.7 to almost 23 million: two extra years cost seven million.