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

Say you take out a fixed interest rate loan for *L *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 *M *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 *r *(expressed as a decimal), and (2) the number of monthly payments *n *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.