One question I’ve been wondering lately is “is it better to buy a home sooner or later?” If you buy it sooner, you get to avoid the rent payments you would otherwise have to make. If you buy it later, you increase your downpayment size (and potentially reduce both your interest rate and your mortgage insurance payments), which can dramatically reduce the total of your mortgage payments. But which is better? Is there a best time to buy?

To attempt a proper comparison, I looked at the Total Cost of Housing over a 50 year period, assuming the following values (typical for a small 2 bedroom home in SF Bay Area):

• The home costs \$700K
• Assume that your monthly mortgage payment + other housing costs below is fixed at \$4000, and rent on a similar place is \$3000/mo. You pay this amount till it’s paid off.
• Assume you can save at most \$2000/mo toward your downpayment and at the beginning have \$0.
• Interest rate 4% (fixed, for simplicity)
• Property tax + home insurance is \$477/mo
• Mortgage insurance: varies with your downpayment (about \$208–572/mo). For downpayments of at least 20% it is not required.
• Assuming closing costs on the loan are about \$10000
• Assuming HOA fees and home maintenance are \$0 for simplicity

I wrote a Python script taking these all into account to compute Total Cost of Housing over 50 years for various downpayment sizes. Here is what I found:

Transitioning at month 0: Downpayment: \$0 (0%)
Total Cost of Housing: \$1951911.80927

Transitioning at month 16: Downpayment: \$32000 (5%)
Total Cost of Housing: \$1845873.48646

Transitioning at month 35: Downpayment: \$70000 (10%)
Total Cost of Housing: \$1826138.74022

Transitioning at month 53: Downpayment: \$104000 (15%)
Total Cost of Housing: \$1827415.89504

Transitioning at month 70: Downpayment: \$138000 (20%)
Total Cost of Housing: \$1757611.99108

Transitioning at month 86: Downpayment: \$172000 (25%)
Total Cost of Housing: \$1834502.99108

Transitioning at month 175: Downpayment: \$350000 (50%)
Total Cost of Housing: \$2237049.99108

Transitioning at month 351: Buy on cash, no loan required
Total Cost of Housing: \$2571773

Rent for all 50 years
Total Cost of Housing: \$1800000

While I made many assumptions in my model which may vary in individual cases, these results turned out to be exactly what I expected: a 20% downpayment is the “magic number” that achieves the best Total Cost of Housing: it gets you out of your rental relatively quickly, and you aren’t on the hook for mortgage insurance, so you’re able to use that cash to pay down your loan faster. But other values like 5%, 10%, 15%, and 25% are actually very similar, less than a 5% difference. A 0% downpayment is a bad idea, a 50% downpayment is worse, and saving up to buy the entire house in cash is a terrible idea.

Renting forever is actually a very competitive option on the 50 year timescale, but becomes less attractive as it’s expanded to 80 years: now renting is \$2.9M, while the purchased home at 20% downpayment stays down at \$1.9M. This supports the common wisdom that buying a home mitigates longevity risk in retirement. Additionally, the house is part of your wealth and can be sold or inherited, which may justify the additional cost even if you die young.

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