The less payments you have to make, the more of your cash you get to keep. Dave Ramsey's "debt snowball" is probably the way to go, pay off the smallest shit first, then use that extra cash flow to pay off he largest. Your dad is saying to not worry about your student loans because historically they have the lowest interest rates ... but interest rates today are low as shit, and its not like you are getting that money back investing in savings / CDs / stock market right now, so I would say paying off your student loans only has one result: better cash flow.
Also, give yourself a couple thousand dollar "shit happens" fund to pay for any unforeseen expenses, you don't get any bonus points for paying off your loan early if you are flat fucking broke and have to take out another loan to pay for something you could have paid for out of pocket.
The only debt I've ever carried is my mortgage, I pay my credit card bill off in its entirety every month ... makes it a lot easier to not worry about money.
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