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.
By AdminDrafted with AI writing toolsUpdated Checked examples: 4
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.
Multiply the payment you can afford by the annuity factor (1 − (1 + r)^−n) ÷ r, where r is the annual rate ÷ 1,200 and n the number of monthly payments. At 7.5% over 20 years, 1,500 a month repays a loan of 186,198.20. Add your down payment to get the highest price: 236,198.20 with 50,000 down.
That loan is the ceiling your payment budget sets. A lender also checks your income, existing debts, credit and any collateral before approving a loan.
Each future payment is worth less today, because part of it pays interest for the months in between. Discounting all of them to today gives the loan they can repay:
The 240 payments total 360,000, so 173,801.80 of them is interest. The down payment raises the price you can pay but sits outside that repayment total.
At a zero rate there is nothing to discount, so the loan is simply payment × months: 1,000 a month for 12 months repays 12,000. For one month at 12% a year, a 1,010 payment repays 1,000, because the month's interest is 10.
Microsoft's PV documentation describes the same constant-payment, constant-rate relationship. =PV(7.5%/12, 240, -1500) returns 186,198.20; the payment is negative because it is money paid out.
Each row keeps the payment at 1,500 a month for 20 years. Loan and interest are rounded to two decimals:
| Annual rate (%) | Affordable loan | Total interest |
|---|---|---|
| 6.5 | 201187.51 | 158812.49 |
| 7.5 | 186198.20 | 173801.80 |
| 8.5 | 172846.26 | 187153.74 |
A higher rate sends more of each payment to interest, so the same payment repays a smaller loan. Each percentage point here moves the loan by about 7%.
Read the other way, keeping the 186,198.20 loan at 8.5% instead of 7.5% raises the payment from 1,500.00 to 1,615.87 a month.
Yes, 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 and 214,526.44 over 30.
Going from 20 to 30 years adds 28,328.24 of borrowing, but the payments total 540,000 and interest rises from 173,801.80 to 325,473.56. Compare the payment count and total interest along with the loan size.
The formula covers principal and interest only. Property tax, insurance and fees come out of the same monthly budget, so subtract them before working out the loan.
Existing debts share the budget too. Suppose you cap total debt payments at 1,800 on a gross income of 5,000 a month, a 36% debt-to-income ratio. If other loans already take 300, 1,500 is left for the new one.
Lenders run the same check with their own limits. The CFPB explains debt-to-income ratio as monthly debt payments divided by gross monthly income; the acceptable limit depends on the lender and the loan product.
Count as down payment only the cash you can put toward the price, since fees paid at closing come out of the same savings.
The rate is fixed for the whole term and each payment falls at the end of a month. The term must come to whole months, so 2.5 years (30 payments) works and 2.4 years (28.8) does not. A lender's rounding can change the final installment slightly.
Use the loan EMI calculator when the loan amount is known and the monthly payment is the unknown. The mortgage calculator adds property tax, insurance and other housing costs.
Checked against: Microsoft PV function documentation example: PV(0.08/12, 12*20, 500) = −59,777.15
Checked against: 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).
Limits depend on the lender and loan product. The CFPB defines debt-to-income ratio as all monthly debt payments divided by gross monthly income; it does not give one approval threshold for every loan. For example, 1,800 of debt payments divided by 5,000 of gross income is 36%. That arithmetic example is not an approval rule. This calculator starts from your chosen payment budget and does not check income, credit history or lender eligibility.
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.
For planning only. Lenders, tax authorities and markets apply their own rounding, fees and rules; confirm figures with them before you commit.
This calculator includes 4 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.