I think it's a bad idea to borrow money for an airplane.
I've been in debt before — "responsible" debt, as some people here would describe it, not like up to my eyeballs or anything — and I don't like that feeling. It's a lifestyle choice, and I think life is much less stressful without having any payments.
Granted, I'm a weirdo. I'm 34 years old and paid off my house when I was 33. That was the big impetus for starting my flight training. When you have a good income and don't owe anybody a dime, you can do anything you want, including waking up one day and saying, "I wanna be a pilot!" Your options are wide open.
From a mathematical perspective, I understand the appeal of playing an interest-rate spread. But the spread on that money isn't worth the stress of having a payment every month — at least, not to me. It's just a personal choice. I can sleep better at night in a paid-off house, with a couple of nice paid-off cars in the driveway, flying a paid-off airplane than I ever could with payments owed to a lender on all those things.
Other folks might not find that same sense of peace from it ... but it works for me.
And I also think when people say "I can borrow money at 4% and get a 15% return on that money," that's a very oversimplified, unsophisticated equation because it doesn't factor in your risk at all. Every investment carries some risk, and you've got to precisely calculate that risk over a certain time frame if you're going to be honest about it mathematically. Your risk-adjusted return won't be anywhere near 11%, most likely, when you actually put the numbers together.
Could the interest spread still work after risk is mathematically factored in? Sure! But to me, it's just not worth the added stress of being in debt to someone. Other people might not have any problem with it, though.
So to the original poster, my recommendation would be to be patient and pay cash for the airplane. It shouldn't take you very long to save up $10k more, especially if you took a part-time job or found some other way to boost your income in the next few months.
And if I'm wrong about it, and flying around in a paid-off airplane turns out to be awful, you can always go get a loan later on. There's never a shortage of bankers willing to take your money if you just hate how it feels in your pocket