Simple Mathematics To Know For Investing

Mathematics, or math/maths, depending on which part of the world you came from, is a subject which almost all of us had encountered in school, and somehow developed into a sort of love-hate relationship with it. However, like it or not, maths (I shall use this short form for this post) is inescapable from our daily lives, such as calculating how much change to get back for a $3.50 meal with a $10 note, and whether two six-inch pizzas are equal to a 12-inch one, etc.

For investing, I shall present two maths concepts to better your knowledge.

 

(Picture credit: athree23 from pixabay.com)

 

#1: Compounding

The famous physicist Albert Einstein once quoted that compounding is the eighth wonder of the world. Yet, several people did not know that there is a second part to the quote, which is “he who understands it, earns it…he who doesn’t…pays it”.

Let us understand the basics of compounding. Supposedly, you deposit $1000 in a financial instrument that pays you a 5% returns every year. After one year, you would have a total of $1050 ($1000 + (5% of $1000 = $50)). After the second year, you will get $1102.50 ($1050 + (5% of $1050 = $52.50)), and so on. For any given number of years (n), the compounding formula is:

P + (1 + r) ⁿ, where P is the principal (the initial $1000), r is the returns (5%) and n is the number of years.

The above illustration fits into the “he who understands it, earns it” narrative, but compounding also has a dark side to it, which is the “he who doesn’t…pays it” part. How so?

Instead of returns on the r, replace it with the bank interest charges that you need to pay for a loan, or the annual inflation rate. Imagine taking out a loan that has double digit interest rate, or the value of your $1000 today becoming $995 next year.

Hence, there are two lessons to be derived here; one is to avoid high interest-bearing loans, and the other is to invest your monies with decent returns instead of keeping it and getting eaten by inflation.

 

#2: Percentage Gain And Loss

I came across a maths scenario that goes like this:

I had lost 50% this year, so I need to gain 50% back to make it even.

If you remove the “%” behind, yes that is correct, but in a percentage, it is based on something and not an absolute value in itself. Using the scenario mentioned, I had lost 50% of $1000 which is a $500 loss and that means I have $500 left. Making it back 50% of what I had left (50% of $500 = $250) is only $500 + $250 = $750, and I still have a shortfall of $250 to the original $1000.

For percentages, the formula requires two values: the initial and the final. Thus, percentage change is:

(Final value – Initial value) / Initial value x 100%

So, to go back to $1000 from $500, the actual required percentage gain would be:

($1000 - $500) / $500 x 100% = 100%

Putting in perspective, here are the percentage losses and the actual required percentage gains to break even:

Percentage Loss	Actual Percentage Gain to Breakeven
10%	11%
20%	25%
30%	43%
40%	67%
50%	100%
60%	150%
70%	233%
80%	400%
90%	900%

 

After looking at the table, some of you may feel daunted by the prospect of losses and the subsequent larger jump to return. For a share price drop of say, 30%, 43% is needed to go back to breakeven, and some viewed a 43% jump is a tall order.

But there are numerous examples of prices that recovered, and then eventually surpassed the original price. This is true for counters that have strong fundamentals, whose prices were, to say the least, temporarily crashed due to bad news that could possibly be affecting only for a short term, and this presented a good opportunity to average down and load up.