mardi 14 août 2018

The shocking math of accumulation

The shocking math as to why vampires must be rich? 

There's a two main mathematical formula that determines on average the expected gains of any vampires. The composed interest accumulation formula focus on the accumulation of a Lump Sum amount for a number of years. The other is the future value of a serie of contributions.

A vampire have thus a lot of possibility to becoming rich. Either he can invest a lump sum of money or a smaller contribution over a period of years. A third possibility is anything in between. Let's explore the vampire timeframe first of a 100 years of investing.

Knowing that the past last century rate of return for a all equity was in excess of 10%, a 73$ investment would be enough to be a millionnaire. Else, the vampire with less than 10$ to spare each year would be a millionnaire also. All in all, it's super easy for a vampire to become rich.

From the above table, we can compare the lump sum strategy to a contribution strategy. The Lump Sum requires 11%/15%/21% less contribution at 10%/7%/5% interest rate. However, the lump sum is 10x/15x/21x more than the yearly contribution strategy. If you are able, it makes sense to fund early and have lower contribution in the future. I haven't read anyone doing it except when in retirement. For a person to be able to act on having lower contribution in the future, we need to have a well though out plan, to be able to live frugally at the beginning and be able to live expensively at the end. It is a rare combination. 

Over 100 years, it is staggering the impact of interest. It requires 50x more contribution to fund a million at a conservative asset allocation than an aggresive one. If we look at Lump sum, it takes 100x more lump sum to get there.

Now let's see over a human life of 35 years investment:

In order to retire a millionaire, we would require about 36k/94k/181k to compound to 1 million. The impact of interest rate is still very much felt.

The way I think about it, if you were able to split at your death 1,2 million and that you would have 3 childs and 9 grand-childs, then each grand-childs would be able to become millionnaire at age 65 easily.

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