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Read my post just above yours. It's a principal paydown loan, he is not paying 12% on 25k each year. So if he invests the full 25k and doesn't touch it, then as he gets paid (not from stocks, from work) and he uses that non-invested money to pay back the loan, he will only need to achieve 6% or so to make money.
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This doesn't make any sense. You are, in effect, claiming that using "non-invested money" to pay back the loan is costless. Ignoring risk, you have to evaluate the merits of an investment by looking at the return on the investment and compare it to the cost of funds required to fund the investment. When the return is lower than the cost, you can't just wave your hands and say that there is some external source of (costless) funds that will be used to pay down the loan while keeping the investment intact.
Opportunity cost FTW.
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it isn't a HORRIBLE idea.
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Yes, yes it is.
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To Capt Zeebo - I am NOT the OP, I make no claims on stock picking ability.
To you Rico - OP mentioned using this as a savings scheme. So his non-invested money that he is using to pay off this loan is the money that he would be investing on a monthly basis (had he not taken the loan). So essentially he is trading a 25k lump sum to invest now in lieu of saving/investing 830.36 a month for the next 3 years and hoping that after 36 months his stock account is over $29,892.89 (cost of borrowing at 12% on Prosper). Any tax consequences of his investments are not of importance because OP states he would be using the money saved (monthly payment if he didn't take the loan) to invest anyway. The only way taxes might come into play is if OP is making tons of trades. But if he buys the stocks and lets it sit, he is actually saving a lot in commissions versus buying $800 in stocks each month.
Of course the issues are this:
Stock Market returning historical averages
Not needing the money for any emergencies
I am not waving my hands saying money will appear to pay back the loan. The OP himself STATED he would be saving the money in any event, but wants to invest the money now and not wait each month.