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How much can I borrow for a given payment?

Run the mortgage problem backwards: you know what you can afford each month, and you want the loan that payment supports.

Problem

You can spend $1,800 a month on principal and interest. Rates are 6.75% for 30 years. How much can you borrow?

Keystrokes

  1. fFINx≷y
    0.00

    Start clean.

  2. 30g12×n
    360.00

    360 monthly payments.

  3. 6.75g12÷i
    0.56

    Monthly rate.

  4. 1800CHSPMT
    −1,800.00

    The payment, negative because you pay it.

  5. PV
    277,521.63

    Solves for the amount you can borrow.

Answer

A $1,800 payment supports a loan of $277,521.63.

Why it works

Any of the five financial values can be the unknown. With n, i, PMT and FV known, PV gives the present value of all those payments, which is exactly what a lender would hand you for them.

CHS makes the payment negative. Forget it, and the calculator answers with a negative loan, which is its way of saying the directions are mixed up.

Turning it into a price

Add your down payment to the loan amount to get a purchase price. If you put 20% down, divide the loan by 0.8 instead: 0.8÷ right after the answer.

Questions

How much does a lower rate help?

Key the new rate with g 12÷ and press PV again. Each half point is worth several percent of borrowing power at these terms.

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