# Calculating the Monthly Payment on a Loan (Including a Mortgage)

Say you take out a fixed interest rate loan for dollars and have to pack it back in monthly installments (one example of such a loan is a fixed-rate mortgage, one type of loan used to buy a house); what would the monthly payment be?

It turns out there’s a fairly simple formula for calculating the monthly payment M. The only additional pieces of information we need to know are: (1) the interest rate (expressed as a decimal), and (2) the number of monthly payments you’ll be making (for a 30-year mortgage, for example, n=12(30)=360). With all of these inputs, equation (3.10) in Section 3.2.2 of The Calculus of Happiness can be used to calculate M. Alternatively, the calculator below does it for you. Input the required data into the green cells and the calculator will use equation (3.10) to calculate M.

## Limitations

The calculator above assumes the loan is structured as a monthly repayment loan, and that its interest rate is fixed. Changing either of these assumptions would change the output monthly payment.