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Renting or buying a 400,000 home for seven years: net worth of each and the break-even year (illustrative)
| Tool | Rent versus Buy |
| Source | Closed-form level-payment mortgage and compound growth; Kellison, S. G. (2009). The Theory of Interest, 3rd ed. McGraw-Hill/Irwin, New York. The case is illustrative, not a printed example; its cost assumptions are round figures, not data for any place. |
| Level | Undergraduate |
Problem
A home costs 400,000 with 20 % down and a 30-year mortgage at 6.5 %; an equivalent home rents for 2,200 a month. The stay is 7 years, homes appreciate 3 % a year, rents rise 3 % a year and investments return 6 %. Property tax is 1.1 % and maintenance 1 % of the home's value a year, home insurance 1,800 and renter's insurance 240 a year, buying costs 3 % and selling costs 6 %, no income-tax saving. The renter invests the buyer's cash and the monthly difference. Find each one's net worth after 7 years and the break-even year.
Inputs to Enter
- Home price 400,000; down payment 20 %; mortgage 6.5 % for 30 years
- Rent 2,200 a month; stay 7 years
- Appreciation 3 %, rent increase 3 %, investment return 6 % a year
- Simple-mode assumptions: property tax 1.1 %, maintenance 1 %, insurance 1,800, buying 3 %, selling 6 %, renter's insurance 240
Answers
- Cash to buy: down payment 80,000 + buying costs 12,000 = 92,000; loan 320,000
- Monthly rate 0.065 / 12 = 0.005417; payment M = 320,000 i (1 + i)^360 / [(1 + i)^360 − 1] = 2,022.62
- First-year monthly cost: owner 2,022.62 + 700 + 150 = 2,872.62; renter 2,220.00; the renter invests 652.62
- Buyer after 7 years: home 491,949.55, loan balance 289,331.98, net worth 491,949.55 · 0.94 − 289,331.98 = 173,100.59
- Renter after 7 years: 92,000 · 1.06^7 = 138,333.98 plus the monthly differences with growth 55,173.32 = 193,507.31
- Buyer less renter −20,406.72 = starting gap −36,000 + unrecoverable renting costs 204,127.99 − unrecoverable owning costs 188,534.71
- Break-even year 12 (buyer 278,939 against renter 275,610)
Notes
The tool's default inputs are this case; press Submit. Every figure is checked against a separately written numpy model (test_rent_vs_buy.php). Constant rates are assumptions, not forecasts. A calculator for education and analysis, not investment advice.