A simple example of the power of compound interest

There is an urban myth that Albert Einstein, when asked what the most powerful invention by man was, simply replied with “compound interest”. While there is little proof that Einstein actually said that, I believe it isn’t unlikely that the man who helped invent the atomic bomb would recognise compound interest as an incredibly powerful concept.

What makes compound interest so amazing are the seemingly impossible amounts that money can grow to if left for a long enough time. While it is difficult to conceptualise how huge amounts can accumulate to under compound interest, I came across an example the other day that really helps put it into perspective.

Imagine a worm one centimetre long – so not that much bigger than a grain of rice. Every day, this worm grows ten percent longer. So on day one it is one centimetre long. On day two it is 1.1 centimetres long, on day three 1.21 centimetres long etc.

How long will the worm be after one year?

Now, you would have gathered that the answer to this question is going to be a big number. So, how big do you think it will grow? A kilometre? Ten kilometres? Or something audacious like the distance from Durban to Johannesburg?

A one centimetre long worm that grows ten percent longer every day, will stretch from the sun, to Pluto, back to the sun and end on Venus after a year of growing at that rate.

Absolutely mind-boggling, I know. Even after checking this myself it still feels impossible. But far from being just an interesting anecdote, this example does illustrate a very important aspect of compound interest that you can use to your advantage:

Invest early, and invest for a long time.

Compound interest means that your money grows exponentially. In our example above, after eleven months our worm only stretches 12% of the way from the sun to Pluto. The last month of the worm’s growth makes up 94% of its total growth after a year.

What does that mean for you now? It means that it is never too early to start saving. Are you thinking of only starting to save in two years’ time once you have a better cashflow situation? Don’t wait too long – every year you wait now has a massive impact once you want to realise your investment!Image


To rent or to buy your home – what do the numbers say?

Recently a friend spoke to a financial adviser when the topic of renting or buying property came up. The adviser’s opinion was that if you can afford to buy a place, it is always a better option than renting, regardless of the scenario you find yourself in. My friend, having recently just bought a place, disagreed and he felt that there definitely were occasions when the smarter financial decision is to rent. So we decided to put some numbers to it.

1. The model

We put together a simple model that compared the cashflows under two scenarios: one where you buy and the other where you rent the property you live in. First, we projected all the cashflows that you would incur if you were to buy a property. This includes:

  • The expenses you incur upfront (transfer lawyer fees, bond lawyer fees, transfer duties etc.)
  • The deposit you would be required to pay upfront
  • The ongoing mortgage repayments you would need to make on a monthly basis.
  • The ongoing costs you would be required to pay as an owner (rates, levies, water & lights and ad hoc expenses)

We then compare these cashflows to the scenario where you rent the equivalent property. We have assumed that the renter pays an all in rental amount that includes all the ongoing expenses (rates, levies, water & lights etc.) We also then assume that in any month where the total amount the renter pays is less than what the property owner pays (see the four bullets above), the renter invests that difference in equities. Thus, we have assumed that the renter and the owner pay the exact same amounts every month. The renter’s investment into equities is the balancing item that makes the monthly payments from the owner and the renter the same.

Under the owner scenario, we then model the value of the property, less the outstanding amount of the loan, less the commission the owner would have to pay to an agent on sale. i.e. we are modeling what the property owner would receive if they were to sell their property and pay the outstanding balance on their mortgage.

Under the renter scenario, we then model the accumulated value of the equity investment.

Thus we are able to compare the value of the two investments over time: the value of the property (in the case where you buy your property) and the value of the equity portfolio (which is made up of the savings when you rent instead of buying).

2. The assumptions

Now, the big influencer of the results of any model are the assumptions that go into it. We have made a number of assumptions in order to compare the two scenarios. The important ones are:

  • Property value is R1.6 million
  • Prime rate is 8.5% and the buyer qualifies for a loan at prime less 1%
  • The buyer puts down a deposit of 10% of the property
  • The term of the loan is 20 years. The monthly mortgage repayments are then R11 600.
  • The fees and taxes on purchasing the house are R100 000
  • The monthly costs for the property total R 4 300 (Rates, levies, water and lights, ad hoc expenses)
  • The all in rent for the equivalent property is R10 000 per month
  • The monthly expenses and rent rates grow at 6% pa
  • The value of the property grows at 9% pa
  • The equity investment that the renter holds grows at 14% pa

The two big assumptions that might strike you immediately are:

  • The rent assumption versus the mortgage repayment amount. Generally, the cost of renting a property is less than the mortgage repayments. I checked with the property leasing experts and this was the amount that they felt was reasonable
  • The growth rate of property versus equity. Historically, over the long term in South African equity returns have exceeded property returns. It is not unreasonable to assume that an equity portfolio will grow at a faster rate than your property (on average!)

3. The results

The results of the above were interesting, but not that unexpected. Below we have plotted the value of the property less the outstanding mortgage, against the accumulated value of the equity portfolio that the renter would hold. The equity portfolio starts off at a higher value, but somewhere between year 4 and 5 the value of the property overtakes the value of the equity portfolio. So, if the above assumptions were to hold true, the purchaser of a property is better off than the renter from year 5.

Graph 1: 10% Bond

Graph 1: 10% Bond

However, things got a little interesting when we changed the assumption around the amount of the deposit. We then assumed that the purchaser puts down a 50% deposit instead of a 10% deposit in the above scenario. Have a look now at the projected value of the property value and the equity portfolio.

Graph 2: 50% Bond

Graph 2: 50% Bond

In this scenario, if the above assumptions were to hold true, the renter is always in a better position than the property purchaser. This model even allows for the fact that rental costs will eventually exceed mortgage repayments and the renter will need to realise some of their investment portfolio in order incur the same monthly costs as the property owner.

Why is the renter better off now? It would seem counter-intuitive, since conventional wisdom would tell you that it is better to put down a bigger deposit on your property. While it is still a good idea to put down a larger deposit on a property purchase, a smaller deposit does increase the gearing of your returns. Purchasing a property is an investment in property over other assets (in this case, equities). The renter does not choose to invest in property. In the second example, the purchaser puts down a deposit of 50% (R800 000). The renter instead chooses to invest that R800 000 upfront in equities, which in this model, are expected to outperform property growth by 5%.

In the first scenario, equities are still expected to outperform property, but the property purchaser has geared their property returns. The bank has purchased 90% the property for the owner. The property is expected to grow at 9% pa, but the financing charge on the mortgage is only 7.5% pa. So in the first example the property purchaser is better off because they have geared their property returns more than in the second example.

4. Conclusions

Now, please don’t take the above as me advising you to always rent a property over buying it, or to put down the smallest possible deposit on a purchase, that is definitely not the purpose of this post!

On the flip side, yes you could argue against a large number of the assumptions that I have made in the above model. However, what I have set out to do is show that, for a reasonable set of assumptions (and the above assumptions are reasonable), it is possible that renting is a better financial decision than buying.

We live in a world of infinite possibilities, so absolute advice is usually risky. Don’t assume that it is always better to buy than rent. When deciding on whether to buy or rent, look at the circumstances that you find yourself in, and make the correct decision for your situation.

5. Final points

One of the big implicit assumptions in the above model is that the renter is disciplined enough to invest the extra cash they have by renting rather than buying. Not a lot of people are able to do this, especially in South Africa with our terrible savings culture.

There are factors that influence your decision to rent or buy that are not modeled above or do not have a financial impact. I will unpack these in my next post.

And finally, for what it’s worth, I purchased the property I live in, in spite of the above.

Thanks to Warwick Wiseman, Jared Cumming, Mark Leslie and Kim Woods for their help in this post.