There’s an old debate about what is best to do with savings or extra money: use that money to pay off debts such as a mortgage, or to use that money to invest. The answers very depending on the sources, and this article does not tell you which is best, but it DOES take a look at the maths and which approach is more likely to lead to greater wealth in the long run.

Debt has a few variables that we are looking at here:

1. The interest rate

2. The number of payments per period (such as weekly, fortnightly, or monthly payments)

3. The length of the loan

Funny enough, you will notice the amount of the loan is not mentioned above. As it turns out, the amount borrowed does not matter, mathematically. We will demonstrate this with some examples:

**Example 1**

If you have a loan and let’s say the amount borrowed is $100,000. Here are the relevant elements from our list above:

interest rate = 6% per annum

payments = 6-monthly

loan term = 1 year

This means you will payoff the debt after 2 payments, (the first payment is 6 months from now, and the second is 12 months from now). Each payment will be $52,261.08, however the first payment will be $49,261.08 towards the principal and $3,000 towards interest. This is because you have a 6% interest rate, but you are breaking that up over half the year, so you divide the interest by 2, which is 3%. 3% multiplied by $100,000 borrowed means you pay $3,000 towards interest in the first payment. The second payment is also $52,261.08, but that payment applies $50,738.91 towards principal and $1,522.17 towards interest.

So if you add up the total amount of interest paid over that year, you see the total is $4,522.17. Effectively, the interest you really paid on your 6% loan is closer to 4.5%. Funny, right?

**Example 2**

If you stretch out the loan and make more payments per period it changes yet again. Again we’ll say $100,000 borrowed interest rate of 6% but this time:

Payments = weekly (so 52 per annum)

Loan Term = 30 years

In this scenario, the payments would be $138.26 each week, for 1,560 weeks. The total interest paid by the end of the loan is $115,699.03 but look at the individual years. The total interest paid by the end of year 1 is $5,964.31 or 5.96%, which is much closer to the 6% interest rate. The final year (30) only pays interest of $224.33 which is an interest rate of 0.022%, which is very small.

When you average the interest rate out over the 30 years it also comes out to be lower than the 6% average, because you are constantly paying down the principal. If you took the amount of interest paid in the first loan payment which would be $115.38 and paid that amount every week over the same 30 years into an investment account, you would want to make sure it came out to be more than the $115,699.03, because that is your break-even point. In order to come out on top the interest or rate of return you would need on money invested would be a miserly 3.2%. That’s it. 3.2%!

3.2% is currently higher than some __termed deposit rates__ offered by most major banks. The funny thing is that a balanced fund in New Zealand has historically offered somewhere around 5%-6% (or 3.5% after inflation), for quite some time, __according to the FMA__. This means that if you were given the choice to invest money in a balanced fund and expected to earn something like 5% over a long period of time, you would likely come out with more wealth than if you chose to pay down debt, assuming the debt had an average interest rate of 6%.

The common mistake that individuals tend to make is looking at the stated interest rate on debt and comparing it to what investments have done over the past few years. This is actually comparing apples to oranges because debt can only have a finite amount of interest, so you can never save more than the amount of interest owed. Investing is the opposite, you can essentially gain an infinite amount, given enough time. This is the real-life application of compound interest that we keep hearing about. Compounding has a bigger effect, the longer the time period, so that means if you compared a longer-term loan to an investment of the same time horizon, the chances are in favour of the investment because it can compound at such a conservatively low rate of return, but still be do more to grow wealth, compared to paying off more debt.

The winner in this scenario is investing. Paying down debt faster is unlikely to lead to more wealth over the long term. Many people will oppose this view, and we have even written a __counter-point to this article__, to be fair and balanced. Although it's worth asking someone to draw out the maths for you when they recommend paying down debt first, just to see what evidence they have to support their claim.

If this interests you __here is a short video__ explaining the math from another point of view + __a 57 second clip__ look at the benefits of owning a mortgage and why Adele did it.

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