The formula
Renting and buying are not two prices — they are two piles of money over the same years. The formula has two sides. The renting side is simple: add up the rent over the years, letting it rise a little each year. The buying side is four piles minus one: the down payment, the mortgage payments, the yearly running costs (property tax, insurance, maintenance), and the opportunity cost of the down payment — minus the equity you get back when you sell. Whichever pile is smaller wins, and the breakeven year is the first year the buying pile is smaller than the renting pile. That is the whole formula — two piles, one subtraction, one year.
Step 1 — Write down the rent and the home
Start with the two numbers the comparison hangs on. In our worked example the rent is $1,800.00 a month and the home costs $400,000.00. The rent is what you would pay if you keep renting; the home price is what you would pay if you buy. Write them both down, and keep them fixed — the rest of the steps all use these two numbers, and changing one of them halfway through is how comparisons go wrong.
Step 2 — Work out the monthly mortgage payment
A 20% down payment on a $400,000.00 home is $80,000.00, so the loan is $320,000.00. At a 6.50% rate over 30 years the monthly payment is $2,022.62. The payment formula is loan × i ÷ (1 − (1+i)^−360), where i is the monthly rate — 6.50% divided by 12 — and 360 is the months in 30 years. You do not need to work it out by hand: the mortgage payment calculator does it, and the rent vs buy calculator does the whole comparison. Over 7 years the payments add up to $169,900.08.
Step 3 — Add the yearly running costs
Owning a home costs more than the mortgage. Property tax at 1.10% of the home value is $4,400.00 in year 1; homeowners insurance is $1,800.00 a year; maintenance at 1.00% of the home value is $4,000.00 in year 1. Together with the payment, the monthly owning cost in year 1 is $2,872.62 — payment $2,022.62 + tax $366.67 + insurance $150.00 + maintenance $333.33 — against $1,800.00 of rent. That gap is real, but it misleads: part of the $2,022.62 payment is principal, which is equity you keep, not money you lose. Over 7 years the tax, insurance, and maintenance add up to $76,964.70 — tax and maintenance grow with the home value, insurance stays flat.
Step 4 — Add up 7 years of rent
Rent rises. At 3.00% growth a year, $1,800.00 a month is $21,600.00 in year 1, $22,248.00 in year 2, and so on — and over 7 years it adds up to $165,509.18. That is the pile buying has to beat. If rent never rose at all, 7 years of rent would be only $151,200.00 and buying would take until year 17 to break even — so the rent-growth number you pick matters more than most people think. Use the rent you actually pay, and a growth rate you actually believe.
Step 5 — Work out what you get back when you sell
After 7 years the home is worth $491,949.55 at 3.00% appreciation a year. Selling costs of 6% leave $462,432.58, and after the remaining mortgage balance of $289,331.75 the equity back is $173,100.82. That equity is what makes buying catch up: you paid $80,000.00 down and $169,900.08 in payments, but $173,100.82 comes back. The down payment also has an opportunity cost — $80,000.00 at 5.00% a year for 7 years is $28,000.00 of earnings given up — and that goes on the buying pile too.
Step 6 — Compare the piles and find the breakeven year
The net cost of buying over 7 years is down payment $80,000.00 + payments $169,900.08 + running costs $76,964.70 + opportunity cost $28,000.00 − equity back $173,100.82 = $181,763.96. The rent pile is $165,509.18. The gap is $181,763.96 − $165,509.18 = $16,254.78 — renting wins by $16,254.78 at 7 years. But the gap peaks in year 3 at $27,084.17 and then shrinks every year: at year 9 renting still wins by $3,641.42, and at year 10 buying wins by $4,638.10. The breakeven year is year 10 — the first year buying wins. At 15 years buying wins by $68,041.23. If you will stay less than 10 years, rent; if you will stay longer, buy — on these numbers.
What if the home is $300,000?
A cheaper home flips the answer. On a $300,000.00 home the payment is $1,516.96, and buying wins at 7 years by $26,036.12 — the breakeven year is 4. The rent is the same $1,800.00 a month, but the loan is smaller, the running costs are smaller, and the equity builds on a smaller base. The lesson is that the home price matters more than the rent: a $100,000.00 cheaper home moves the breakeven year from 10 to 4.
What if the mortgage rate is 5%?
A lower rate flips the answer too. At a 5.00% mortgage rate the payment is $1,717.83, and buying wins at 7 years by $17,255.32 — the breakeven year is 5. A 1.50-point drop in the rate moves the breakeven year from 10 to 5, because every payment carries less interest and more principal. If you are waiting for rates to fall before you buy, this is the number to watch: the rate moves the breakeven year by years, not months.
The rent that ties the two
At $1,976.78 a month, rent ties buying exactly at 7 years — the gap is −$0.06, effectively a tie. At $1,975.78 the gap is $91.88 (rent wins); at $1,977.78 it is −$92.01 (buying wins). So the question “is $1,800.00 rent cheap or expensive?” has a number attached: $1,976.78 is the line. Below it, rent; above it, buy — at 7 years, on a $400,000.00 home at 6.50%.
The monthly-cost warning
The year-1 owning cost is $2,872.62 a month against $1,800.00 of rent — $1,072.62 more every month. If you stop there, buying looks like a bad deal. But part of the $2,022.62 payment is principal (equity), so the monthly comparison misleads: the honest comparison is the cumulative one, over years, with the equity back subtracted. That is why the calculator compares piles over a horizon instead of months — and why the breakeven year, not the monthly payment, is the answer to “rent or buy?”