You always want to pay off your debt. Any debt at all usually is detrimental to your financial position (unless it is a friendly loan of a few dollars). This is usually because loans always have very high interest rates, at least higher than the interest you can earn from a bank. The main reason is because banks and other lenders take larger risks lending to individuals and demand a higher rate of return whereas banks offer FDIC secured accounts and can offer lower rates.
Often, many people make the mistake of not paying down as much of their debt as possible for whatever reason. I believe there are people who carry over credit card debt even when they have money in their savings account, and what they don't realize is that the interest they earn on their savings is much less than the interest charged on their credit card debt. They would actually be saving themselves the difference if they just withdrew their savings and paid off their debt. Credit cards have especially high interest rates in general because of their flexibility. You have to pay a premium for having that ability to instantly take a loan up to your credit limit and pay it over time.
A common question have is whether to pay down a debt (a mortgage, student loans, etc.) or invest that money to make more money and pay debt later. The analysis is relatively simple: you have to compare the interest rate you have on your loan with how much you expect to earn on your investments. For example, if you have a 15% interest rate on your credit card debt and expect to earn 10% on your investments, it is obvious that paying down your debt will "earn" you more money than investing to pay for it later.
What if the rates are similar or your debt has a lower interest rate? For example, maybe your mortgage is only at a 7% interest rate and you expect to earn 10% over time on your investments. You have to make sure you are comparing after tax numbers for one thing. Interest paid on mortgages are usually tax deductible, meaning you can pay for them with pre-tax dollars rather than after-tax dollars. In other words, the amount of interest you pay times your tax rate is how much tax you would save, whereas if you paid off your entire mortgage balance right now, you would then have to pay the taxes you would have otherwise saved. On the other hand, you will be taxed on any capital gains and dividends you receive from your investments.
So let's say you calculate your after-tax returns to be around 8% for your investments, but your effective interest is around 6% for your mortgage because of your tax savings. It looks like you should invest your money and leave your mortgage to be paid off later. This is where you have to ask yourself how risky your 8% number is. Depending on how much cash you have available to continue making mortgage payments and how long a horizon you are looking at, it may still be better to pay down your debt. Paying down your debt is a sure way to earn that 6% in savings from interest, whereas your investments may turn out poorly. You run the risk of losing money if you choose to invest rather than save, but you also have the chance to make a lot more money as well. It depends on your risk tolerance. As with everything, there is reward associated with risk, but you never want to take on too much risk.
In most situations, I believe it is better for people to pay down any debt they have as fast as they can. The special exception is if you have debt at a low interest rate for a long time (e.g. 5-8% for 20-30 years). In those cases, it may be better to park your money into the S&P 500 and just let it grow for a while. It is even better if you can put them in an IRA to get the tax advantages associated with them. You just have to make sure you have enough cash in the meantime to make your regular payments by the due date and avoid any late fees or other extra costs.
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