RightFiguresWhat the result means
Buying leaves more wealth when the buyer’s terminal nominal wealth is higher. Renting leaves more wealth when the renter’s figure is higher. An equal result is the same wealth. The result is not a comparison of rent paid with the mortgage payment.
Both people pay housing from income. The renter starts by investing the down payment and the cash closing costs. Each month, whoever pays less invests only that month’s difference. Savings from earlier months stay invested. Interest is credited at the annual opportunity rate divided by 12, half up to the cent, before that month’s deposit.
Sale price
The home sells for:
purchase price × (1 + annual appreciation) ^ (holding months ÷ 12)
That power is rounded half up to the cent once, at the sale. Twelve months uses exponent 1. Eighteen months uses 3/2. One month uses 1/12. A rate of exactly −100% is rejected. At that rate the factor would be zero for every holding period.
Selling costs are that sale price times the percent you enter, plus any flat selling cost. Net proceeds are the sale price minus selling costs minus the remaining mortgage balance. Proceeds can be negative. That shortfall stays in the buyer’s wealth.
The mortgage
The regular payment is the fixed-rate annuity used by the amortization calculator, half up to the cent. Each month credits balance × annual rate ÷ 12, half up. The scheduled last month pays whatever principal and interest remain. If that final payment is more than twice the regular payment, the comparison is rejected and no wealth result is shown. A $100 loan at 25% for 50 years is rejected: the regular payment is $2.08 and the forced final payment is $102.08.
Purchase closing costs are cash. They are not added to the loan. PMI is excluded. IRS Publication 936 and Publication 523 are the tax publications this comparison does not apply.
A seven-year example
A $400,000 home, $80,000 down, 6% for 30 years and $12,000 of cash closing costs. Annual tax is $4,800, insurance $1,800 and maintenance $2,400. Rent starts at $2,200 and rises 3% a year. Renters insurance is $180 a year. Appreciation is 3%, the hold is 84 months, selling costs are 6% and the opportunity rate is 5%.
The sale price is $491,949.55. Commission is $29,516.97. The remaining balance is $286,846.22. Buyer wealth is $175,586.36. Renter wealth is $156,495.55. Buying leaves $19,090.81 more.
Held for one month, a $300,000 home with $60,000 down, $20,000 of closing costs, 6% selling costs and $1,800 rent leaves the renter $37,800.00 ahead. That figure is the selling cost, the closing costs, the first month of interest and the tax and insurance, minus the rent.
Sources & review
- Closing disclosure explainer — Consumer Financial Protection Bureau
- Publication 936, Home Mortgage Interest Deduction — Internal Revenue Service
- Publication 523, Selling Your Home — Internal Revenue Service
Last reviewed: . The formula is reproduced above so you can check the math independently.
Educational estimate only. A lender’s payment, a tax deduction and a local selling cost can differ from the amounts you enter.