Buy vs Rent: Net Worth Compared

Two households start with the same money and spend the same each month. One buys and one rents, and whichever spends less in a month invests the difference. Set the prices, rates and costs, and the page follows both month by month and says when, if ever, buying pulls ahead. Every figure is worked out in the tables below the charts.

Worked example — Buy vs Rent: Net Worth Compared

Loan	320,000
Monthly interest rate r	0.004167
Monthly mortgage payment	1,717.83
Buyer's cash up front (deposit + purchase costs)	91,000
Price-to-rent ratio	18.5
Renting, cash paid in year 1 (rent + insurance)	21,800
Home value after 10 years	537,567
Mortgage left after 10 years	260,295

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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Lesson

The theory — Buy vs Rent: Net Worth Compared

A fair comparison starts both households with the same cash and gives them the same budget every month. The buyer spends it on a mortgage, a loan repaid in equal monthly payments M = L·r(1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), where L is the loan, r the monthly rate and n the number of payments, plus the costs of owning. The renter pays rent and invests everything the buyer spends beyond it, including the deposit; when owning costs less, the buyer invests the difference instead. Net worth is what each would have if everything were sold: the home less selling costs and the loan still owed, or the investments. The break-even year is the first year the buyer's net worth reaches the renter's.

What each symbol means

M: the monthly mortgage payment. Part interest, part principal, and the principal share grows each month
L: the loan, the price less the deposit
P/R: the price-to-rent ratio, price ÷ a year's rent. Other things equal, high favours renting and low favours buying
g: home price growth a year. Compounds on the whole price, not only on the deposit
i: the investment return a year. What the renter's money, and the buyer's deposit, could have earned

Assumes: Both households invest every spare unit of money at the same return and never spend it; neither moves house again before the horizon; the mortgage rate is fixed for the whole term. Real households often do not invest the difference, and a comparison that assumes they do flatters whichever side spends less each month: at the balanced settings, the renter for the first 17 years.

One percentage point decides it 🖖

Press Balanced. After ten years the buyer is ahead by 2,952 on a 400,000 house, which is a tie by any honest reading, and the grid under the charts shows how fragile it is. Lower home price growth from 3% to 2% and buying takes 26 years to catch up instead of 10. Raise the investment return from 6% to 7% and it never catches up within 40 years. Both are ordinary assumptions nobody can promise for thirty years. Any single answer rests on one choice of both, and the grid shows which one yours rests on.

Buying and selling costs make a short stay a loss 🖖

Press Moving in 3 years. The same house, the same assumptions, and the buyer ends 22,898 behind, where after ten years the buyer is 2,952 ahead. Buying costs 11,000 going in, as 2% transfer tax and 3,000 in fees, and selling costs 21,855 coming out, 5% of the value at sale, paid whether the price rose or fell. Three years of growth, 37,091, covers those two, but not those two plus three years of owning costing more than renting. At these settings the buyer's position improves every single year, from 28,466 behind after the first, so the question is how long you stay rather than whether buying is good.

Principal comes back, but the deposit costs you 🖖

Comparing rent with the whole mortgage payment is the wrong comparison, because part of the payment is principal and comes back when you sell. So take it out. At Balanced the owner pays 29,923 in the first year, of which 4,721 is principal. But the 80,000 deposit is sitting in the house, not in investments, and the growth it and the repaid principal give up is 4,927, a little more than the principal itself. The owner's money that does not come back is 30,129 in the first year, before any rise in the price and leaving out the one-off costs of buying and selling, 7.53% of the price, against the renter's 22,016. Both views are right: principal is saving, and the deposit is not free. The table prints both for any settings you choose.

Problem solved in full

What owning really costs in the first year 5 steps
A 400,000 home is bought with 20% down and a 30-year mortgage at 5%. Prices rise 3% a year. Property tax and maintenance are 1% each of the current value a year, charged monthly, and insurance is 1,200 a year. The alternative is renting at 1,800 a month, with 200 a year of renter's insurance and a 3,600 deposit that is returned, and investing at 6%. Find the monthly payment, the owner's cash cost in year 1, and how much of it does not come back. Press Balanced to check.

Open this problem in the tool
1. The loan is 320,000, the monthly rate 0.05 ÷ 12 and the number of payments 360:
  
  $M = \frac{L r ( 1 + r ) ^{n}}{( 1 + r ) ^{n} - 1}, L = 320000, r = \frac{0 . 05}{12}, n = 360 \Rightarrow M = 1717.83$
2. In year 1 the owner pays twelve payments, split into interest and principal, plus the running costs:
  
  $12 M = 20614 = 15893 + 4721, 15893 + 4721 + 4055 + 4055 + 1200 = 29923$
3. Principal is not spent: it comes back in the sale. But the deposit and principal would have grown if invested, and that growth is lost:
  
  $29923 - 4721 + 4927 = 30129$
4. The renter's year: rent, insurance, and the growth given up on the 3,600 rental deposit:
  
  $21600 + 200 + 216 = 22016$
5. As a share of the price, the owner's unrecoverable year is:
  
  $\frac{30 129}{400 000} = 7 . 53%$
Answer

The payment is 1,717.83 a month. The owner pays 29,923 in cash in year 1, and the money that does not come back is 30,129, a little more than the cash itself, 7.53% of the price, against the renter's 22,016. The owner is 8,113 behind on the year before the price moves, and whether buying wins depends on the price rising enough to make up both this and the costs of buying and selling, which is the sensitivity grid's question.

$M = 1717.83, 29923 vs 30129$

By the 42Math team · Reviewed against published sources. Corrections welcome.