Find how much you can borrow from the monthly payment you can afford at your rate and term, and the price your down payment then buys.
A payment of $1,500.00 a month for 240 months supports a loan of $186,198.20; with your down payment that buys up to $236,198.20. Of the $360,000.00 you pay in total, $173,801.80 is interest.
| Month | Payment | Principal | Interest | Balance |
|---|---|---|---|---|
| 1 | $1,500.00 | $336.26 | $1,163.74 | $185,861.94 |
| 2 | $1,500.00 | $338.36 | $1,161.64 | $185,523.57 |
| 3 | $1,500.00 | $340.48 | $1,159.52 | $185,183.09 |
| 4 | $1,500.00 | $342.61 | $1,157.39 | $184,840.49 |
| 5 | $1,500.00 | $344.75 | $1,155.25 | $184,495.74 |
| 6 | $1,500.00 | $346.90 | $1,153.10 | $184,148.84 |
| 7 | $1,500.00 | $349.07 | $1,150.93 | $183,799.77 |
| 8 | $1,500.00 | $351.25 | $1,148.75 | $183,448.52 |
| 9 | $1,500.00 | $353.45 | $1,146.55 | $183,095.07 |
| 10 | $1,500.00 | $355.66 | $1,144.34 | $182,739.42 |
| 11 | $1,500.00 | $357.88 | $1,142.12 | $182,381.54 |
| 12 | $1,500.00 | $360.12 | $1,139.88 | $182,021.42 |
This is the EMI formula solved for the loan amount.
This works the EMI formula backwards. Given the monthly payment you can afford, the largest loan it repays is P = M × (1 − (1 + r)^−n) ÷ r, where r is the monthly rate and n the number of payments; this is what Excel's PV function returns. Adding your down payment gives the highest price you can pay.
With the defaults, 1,500 a month for 20 years at 7.5% supports a loan of 186,198.20, and 50,000 down lifts the price you can afford to 236,198.20. The 240 payments total 360,000.00, of which 173,801.80 is interest.
The result is the ceiling your budget sets. Lenders also limit the payment by your income through the debt-to-income ratio, and property tax, insurance and fees come out of the same monthly budget.
Checked against: Microsoft PV function documentation example: PV(0.08/12, 12*20, 500) = −59,777.15
Checked against: Python decimal (prec 50) present value of an ordinary annuity
Checked against: M × n when there is no interest
Checked against: 1010 / 1.01 by hand
Multiply the payment by the annuity factor (1 − (1 + r)^−n) ÷ r. At 8% over 20 years, r = 0.08 ÷ 12 and n = 240, so the factor is 119.55 and a payment of 500 a month supports a loan of 59,777.15. Microsoft's documentation for Excel's PV function gives the same figure for PV(0.08/12, 240, 500).
In the US, the CFPB suggests keeping total debt payments at 36% of gross monthly income or less and housing costs at 28% to 35%, though some lenders go to 43% or higher. Fannie Mae's standard maximum is 36%, rising to 45% with credit-score and reserve requirements and to 50% for loans underwritten through Desktop Underwriter. On a gross income of 5,000 a month, 36% is 1,800.
A higher rate means more of each payment goes to interest, so the same payment supports a smaller loan. Over 20 years, 1,500 a month supports 201,187.51 at 6.5%, 186,198.20 at 7.5% and 172,846.26 at 8.5%: each percentage point costs about 7% of the loan. The chart shows the full curve for your payment and term.
Yes, but with diminishing returns and much more interest. At 7.5%, 1,500 a month supports 161,810.14 over 15 years, 186,198.20 over 20 years and 214,526.44 over 30 years. Going from 20 to 30 years adds 28,328.24 of borrowing but raises total interest from 173,801.80 to 325,473.56.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 4 worked examples whose answers come from independent sources; for example, “500 a month for 20 years at 8%” is checked against Microsoft PV function documentation example: PV(0.08/12, 12*20, 500) = −59,777.15.
Microsoft Excel PV function; Consumer Financial Protection Bureau — Debt-to-income ratio.
For planning only. Lenders, tax authorities and markets apply their own rounding, fees and rules; confirm figures with them before you commit.
4 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
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