ParHow to calculate a mortgage payment
A fixed-rate mortgage is the textbook time-value-of-money problem: you know how much you borrow, the rate and the term, and you want the payment.
You borrow $350,000 for 30 years at 6.5% a year, paid monthly. What is the monthly payment?
Keystrokes
- fFINx≷y
Clears the five financial registers so nothing from an earlier problem sneaks in.
- 30g12×n
Turns 30 years into 360 monthly payments and stores it in n.
- 6.5g12÷i
Turns the 6.5% yearly rate into a monthly rate and stores it in i.
- 350000PV
The amount you receive from the lender today.
- PMT
Solves for the payment.
The monthly payment is $2,212.24. It shows as −2,212.24 because it’s money leaving your pocket, the opposite direction to the 350,000.00 you received.
Why it works
The five financial keys, n, i, PV, PMT and FV, describe one stream of money. Store any four and the fifth is the one that makes the stream balance. Here FV is zero because the loan is paid off at the end, and fFINx≷y set it to zero for you.
g12×n and g12÷i are shortcuts for the conversions every monthly loan needs. They multiply years by 12 and divide the yearly rate by 12, and store the result in one step.
Common mistakes
Typing 6.5 into i without g12÷i treats it as 6.5% a month, and the payment comes out at over $22,000.
Giving PV and PMT the same sign. The calculator then can’t find a balance and shows an error, because money has to flow both ways.
Forgetting fFINx≷y. A leftover FV from an earlier problem quietly turns your mortgage into a balloon loan.
Taxes, insurance and PMI
The payment above is principal and interest only. Lenders usually add a share of property tax, homeowner’s insurance and sometimes mortgage insurance. Add those monthly amounts to the result to get what your statement will show.
Questions
Why is the payment negative?
Financial calculators sign money by direction. Money you receive is positive and money you pay is negative, so a loan you receive (PV positive) is repaid with negative payments.
How do I do a 15-year mortgage instead?
Key 15 g 12× in place of 30 g 12×. Everything else stays the same.