Klevah™ - Formula Phone

Formula Phone

This page is for advanced users in the cohort who want to learn about complex formulae.

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Phone Maths Future Value The Price is Right
The Rule of 72 Back to Home

Phone Maths

₿ There is a lot than can be learned by doing phone maths. Just doing the maths may be worth more than the answers you get. If you want to calculate the opportunity cost of leaving money in savings, or spending it, then just ask AI questions Click here.

₿ Alternatively, open your phone calculator and use this formula: The dollar amount you have now, multiplied by the rate of the investment plus one, to the power of (x^y or xy or ^ in calculator) the number of years of the investment, equals the dollar amount after those years of investment. Otherwise put: $dollars now x (rate + 1) ^ years = $Future dollars. Or in brief: $Now x (r+1) ^(y) = $Then.

₿ For example, if you invested $10,000 in a US share fund that earned 11% a year for 20 years you would have $81k at that point (before tax). $10,000 x 1.11^(20) = $81k. If you used savings or mortgage offset of 5% p.a. (a very high number for 20 years of interest rate levels) then you would have $10,000 x 1.05^(20) = $27k (before tax). Save these calculations in your phone calculator history for easy recall.

₿ Once you have done that you can make these calculations faster than AI can. In this case the shares reach 3 times as much as the savings. The generous savings interest rate of 5% has not tripled the original investment, while the share investment is over 8 times. 11% is the average return for the US market over the last 30 years. That is the world’s most held and basic share investment. Share returns for something as large and diverse as the US market become more likely to hit their historical rate the longer you hold the investment. In the short term there could be a crash, or spike, or anything in between. These calculations assume a smooth increase.

₿ Download the Vanguard Index Chart to see how shares have performed relative to other asset classes over the last 30 years. Click here.

Future Value

₿ Another fairly easy formula can give you the future value of a consistent investment or saving amount per year.

₿ Plug in the formula: $Dollar amount invested each year x ((((1 + r)^y)-1)/r) = $Future amount. If you invest $10,000 per year for 20 years at a rate of 11% p.a. then you would have: $10,000 x ((((1.11)^20)-1)/0.11) = $642k. Using a savings or offset interest rate of 5% p.a. gives: $10,000 x ((((1.05)^20)-1)/0.05) = $331k. In both examples $200k has been invested. The shares gained $442k (before tax) and the interest gained $131k. That is a massive difference. If you want to calculate a lump sum to begin with, and then make ongoing contributions, add formulas 1 and 2 together.

₿ You can ask AI for answers Click here. but if you enter these calculations into your phone calculator then you can go back in your history and adjust the variables to test other numbers even faster. This might help stop impulse purchases. Or maybe not.

₿ Please feel free to email us about your experiences. thestockscholar@klevah.com.au

₿ How well you save is a crucial factor in how much investing success you can have. Having the knowledge to see the big financial picture could help with having the discipline to save. If you already have a sensible investing plan, then saving money is most of the battle. The best investments on Earth are powerless to help you without enough money to put in them. Having said that, starting small is a whole lot better than not starting at all.

The Price is Right

₿ Playing around with these calculations can help you understand what is possible. If you know the dollar value that you want to target in the future then play around with the other variables and play ‘The Price is Right’ until you can see what it takes to achieve it.

₿ You might want $1m via investing at an expected 9% after tax annual rate for twenty years. Put the formula in your phone and make guesses of how much you need to invest either at the start or over time to hit the $1m. Repeat your guessing, going higher or lower until the result is $1m. Now you have your figure. It won’t take long. This can be done for any of the variables and avoids plugging in a much bigger formula. The more you calculate these scenarios yourself the more you will internalise, or gain a feel for, financial reality.

₿ The NYSE FANG+ index has had returns of about 28% p.a. over the last 8 years as an extreme example. Don’t calculate that – it will make you feel intense FOMO and possibly even teleport you to an impossible financial reality.

The Rule of 72

₿ The Rule of 72 is a way of using mental maths to calculate compound growth. The rule says that if you divide 72 by the percentage rate of savings/investment p.a. then you will get the approximate number of years it takes to double your money.

₿ A 6% p.a. rate will double your money in 12 years (72/6 = 12). Then you know you will have four times your money in 24 years and eight times in 36 years (before tax). If you can get a 12% return then when will you have eight times your initial investment? It takes 6 years (72/12) to double, 12 years is quadruple, 18 years is the answer (approximately). Using higher percentage returns causes the Rule of 72 to overstate the compounding more.

₿ In reverse, for experts, how long does it take to get 10 times your money at 10%? That rate doubles your money every (72/10) 7ish years. 3 doublings of a number is 8 times and 4 doublings is 16 times. So it takes not too much more than 3 doublings to get the 10 times your money target with over 7 years each doubling (3x7), which is 21-and-a-bit years to fall a bit short. We add in a couple of extra years and guess 23, 24, 25 years? The answer is just over 24 years so any of these is close enough to get the idea. That is quite a calculation to do in your head.

₿ This rule was very handy in the days before having an AI data centre in your pocket. Click here to get a template for using AI to make investing calculations accurately. Click here.

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