Say you want to buy a $500,000 house (guessing if you can rent for $1,500/mo that's a p nice house in your area). Say you can get a 15-year fixed at 3.25%. Say you're in the top tax bracket (39.6%) and your mortgage interest is fully tax-deductible, which it is in most cases, thus rendering your effective interest rate 1.963%.
- Loan of $500,000 (zero down, like with a non-conforming "physician" loan: total $77,625.73 paid in interest over 15 years
- Loan of $400,000 (20% or $100k down): total $62,100.59 in interest (each $100,000 less saves you $15,525.15; this is linear)
- Loan of $300,000 (idk why you would put 40% down, but just to demonstrate your $200k figure): total $46,575.44 paid in interest
Annualizing those figures, that's (1+[15,525.15/100,000])^(1/15) = 0.97% compound, or 15,525.15/(100,000 * 15) = 1.04% simple.
So *if* you were, in essence, to leverage that $200,000 buy-in payment versus the principal the house you would buy, you'd basically just have to beat 1% on it as far as return goes. If you will actually realize that return by literally 150% (prob more like 90% post-tax) in the first year, then it's an absolute 100% no-brainer. I actually have a hard time believe that the buy-in to achieve that high a return could be that low, but remember, I don't know anything about buy-ins.
I am not encouraging you to have debt, nor am I encouraging you to spend $200,000 cash on something which you have not thoroughly analyzed. But, assuming that money that would be used for mortgage is being invested or otherwise providing a return, it's hard to create a pure mathematical argument for paying off simple amortizing debt whose compound equivalent return on money paid over the minimum is less than a 1-year CD, especially versus a staggeringly absurd 83% after tax return, assuming your income goes up (600k-325k)*(1-39.6%) = $166,100 on the first year *alone*.
This of course assumes the returns on the $200,000 buy in will *actually* raise your pre-tax income by $275,000+ a year and pay for itself after 15 months, that the increased income you receive will happen quickly and won't leave you exposed for a significant period of time without cash on hand, and that you're appropriately insured against lost income. But before splashing that amount, you'd better make absolutely darn sure you know what you're getting into.
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