Tag: formula

Posted in Science & Nature

Compound Interest

Posted on by Jinavie

When is the best time to invest? Is it when you have sufficient income and savings that you feel that you have a surplus to invest with?

The correct answer is much simpler: yesterday, with the second best time being today. Because of the magic of compound interest, investing early is the best strategy possible.

Thanks to a simple mathematic rule, compound interest rewards early, small investments more than late, large investments.

The way compound interest works is that after a given time interval (e.g. year), interest (as a percentage of the original investment) is paid out. The next year, interest is paid out again but as a percentage of the new amount. As an example:
1000 x 1.08 = 1080 (end of year 1)
1080 x 1.08 = 1166.40 (end of year 2)
1166.40 x 1.08 = 1259.71 (end of year 3)
…until end of year 10

If we use mathematical shortcuts and convert this into a formula, we can express it as:

(A = future value, P = present value, r = interest rate as decimal, n = number of periods/years)

For example, if we invest $1000 (PV) at an interest rate of 5% (r=0.05) for 10 years, then:

$1000 x 1.08^10 = $2158.92,

meaning we have earned $1158.92 over 10 years. Taking it further, in 30 years our investment would have grown to $10062.66 – ten times our original investment.

Because the formula uses exponents (or powers) for the time, your investments grow exponentially with time. This means that the earlier you invest, the greater your returns become disproportionately. This is why within 10 years, we have more than doubled our initial investment despite a reasonable interest rate and not doing anything else.

A rule of thumb for calculating how long it will take your investment to double is to divide 72 by the interest rate in % (e.g. 7). This is the number of years it will take for your investment to double (e.g. 72/7 = 10.3 years).

On top of this, if we invest small amounts every year, then we can benefit even more from the exponential growth of our investment. For example, just by adding in $100 every year, we end up with an additional $564.55 of investment earnings at the end of 10 years – a 50% increase in returns.

Unfortunately, mathematics works both ways and compound interest also applies to certain loans, such as credit cards. This means that your debt will grow exponentially unless you aggressively pay it back, making it seem impossible to pay off your credit card debt sometimes.

(This graph shows that investing early and consistently is the best strategy to maximise your eventual earnings. Compare the grey and purple line and you will see that despite investing a third of what Lyla invests total, Quincy ends up with a higher portfolio by retirement.)
Posted in Science & Nature

Marriageable Age

Posted on by Jinavie

When is the right time to get married? According to Professor Tony Dooley, you can use an equation to find the right age for proposing. To do this, take “the youngest age you want to marry” and minus it from “the oldest age you want to marry” then times 0.368. Add this number to the youngest age. For example, if you would consider getting married from age 21 onwards and at the latest 30, your ideal age to marry is: (30 – 21) x 0.368 = 3.312 + 21 = 24.312, thus about 24 years and 4 months old. 

This equation is very practical as it is a modified version of equations used in financial and medical fields. This equation is used to maximise profit while minimising loss using mathematics. It may not sound romantic, but according to Professor Dooley, after you reach the calculated age you should not waste time and ask the hand of the next person you date in marriage.

(Source: http://soulofautumn87.deviantart.com/art/All-We-Need-Is-A-4-Letter-Word-111260511)

Posted in Science & Nature

Quadratic Formula

Posted on by Jinavie

Anyone who has studied mathematics to some degree will know about algebraic equations. An algebraic equation is an equation that can be solved to find the unknown value of x. A quadratic equation is an algebraic equation with x², or in other words has two valid solutions to x. Generally speaking, a quadratic equation can be expressed in the following fashion: ax² + bx + c = 0. a, b and c are constants and the equation can be solved to find x. A quadratic equation is definitely more complicated to solve compared to a linear equation and it can be solved using various means and applications such as factorisation. As these methods are learnt in school and this Encyclopaedia is technically not a mathematics textbook, such methods will not be delved into.

If you have not learnt it already, there is a shortcut method to solving quadratic equations: the quadratic formula. This formula can easily find x if you simply substitute in the values for a, b and c. Of course this formula only works if the solutions are real numbers. The quadratic formula is as follows:

As you can see, because of the ± sign, the formula can be used to find both solutions to a quadratic equation. Even without factorising, it can find the answer as long as you substitute numbers into it on a calculator, making maths class very easy. However, as mentioned above the Encyclopaedia of Absolute and Relative Knowledge is not a mathematics textbook and one should instead learn properly from their teacher, not using the formula until they have been taught it properly.

Posted in Life & Happiness

Formula Of Happiness

Posted on by Jinavie

Ask yourself the following questions using a scale from 1 to 10, where 1 is “not at all” and 10 is “to a large extent”:

  1. Are you outgoing, energetic, flexible and open to change?
  2. Do you have a positive outlook, bounce back quickly from setbacks and feel that you are in control of your life?
  3. Are your basic life needs met, in relation to personal health, finance, safety, freedom of choice and sense of community?
  4. Can you call on the support of people close to you, immerse yourself in what you are doing, meet your expectations and engage in activities that give you a sense of purpose?

Add the scores for 1 and 2. This is P for personal characteristics.
The score for 3 is E for existence (health, financial stability and friendships).
The score for 4 is H for higher order and covers self-esteem, confidence, ambitions and sense of humor.
Now input each score into the following equation:

Happiness = P + (5 x E) + (3 x H)

This gives a score out of 100. The greater your score, the happier you are (over 80 is considered a “happy life”). This formula was devised based on a psychology study of 1000 people. It takes into account the various aspects of life that contribute to your overall happiness and emotional well-being. The study showed statistics such as 40% of men reporting that sex made them happy, while 25% of women reported that losing weight made them happy. Men found more happiness in romance, hobbies and a pay rise compared to women.

Although everyone has a different definition of happiness, there is no doubt that there are common “happiness” factors to all of us and this equation tries to objectively quantify how happy you are in life.

Are you happy?

Posted in Philosophy

Formula Of Love

Posted on by Jinavie

Einstein, considered to be the greatest genius in history, once faced this situation while giving a guest lecture at a university.
A student asked Einstein, who had just finished giving a physics lecture, the following:
“Professor, you have discovered the theory of relativity and managed to formularise it. Could you express love as an algebraic formula?”

Einstein thought for a while, then smiled as he wrote this equation on the board:

LOVE = 2△ + 2□ + 2~ + 4/

The students were confused and asked him to explain it further. He then solved it as shown below:

“The sorrow of having to take a path you must take, yet not being able to resist looking back over and over! The frustration of wanting to follow a path you cannot take! That is love.”

(Source: http://xkcd.com/55/)