The ChoosaBroker Trading Academy

1.5. The Power of Compounding

Course Description

“Compound interest is the eighth wonder of the world,” Albert Einstein only famously remarked.

Most of us can’t dream to be financial wizards. We all have our niches of competence. Some are creatively inclined; some others are gifted conversationalists, while some can run 5 kilometres without fainting. But inclinations aside, there is one major life skill, lack of knowledge about which is hurting us big time.
Financial savviness – especially a sound understanding of the concept of compounding – is essential to thrive in the investing world. Research conducted by the George Washington University shows that a mere one-third of Americans have some notion of the power of compounding. You don’t need to be a maths whiz to get hold of the concept. Just plug in some numbers and see for yourself how compounding can leapfrog you to investing success. In this lesson we will learn about the following concepts:

What is Compounding?

Compounding has been a much reviled concept throughout human history. Both Christian and Islamic religious texts have denounced the practice of creditors charging compound interest. Even in Roman law, compound interest was deemed illegal. But compounding outlived all of these initial resistances to become a substantial force in modern finance.
Compounding is the process by which the value of an investment exponentially increases due to earning interest on both the principal capital and the accumulated interest. The power of compounding is an investor’s best friend, and the optimal way to take advantage is to start saving as early as possible. The earlier you begin, the greater will be the effect of compounding.
Let us assume that you start investing $5,000 a year when you turn 25 with the aim to retire at 65. Also suppose that your investment generates a relatively conservative long-term return of 8% annually. Now, if you take the amount saved and multiply it by the number of years you will save, you will arrive at a figure of $200,000. But as soon as we include compounding in the equation, what we are basically doing is adding the annual 8% return and then reinvesting the proceeds to grow the capital to a whopping $1.30 million!!
Now, in case you are curious what the figure will look like if you begin saving that exact same amount at 35, you will have a much more modest $566,000 at 8% yearly by the time you hit 65. In simple terms, missing out on just 10 years of compound interest can erode your balance by more than half.

Compound Interest Formula

The formula to calculate compound interest is explained below:
FV = P (1 + R/n) ^ (Yn)
Where,
FV = Future value of the investment, or the amount the principal grows to after Y years,
P = Starting principal,
R = Annual interest rate,
Y = Number of years invested,
n = Number of compounding periods per year
Let us look at an example to better understand the calculations involved. If an amount of $10,000 is deposited in to a savings account at a yearly interest rate of 5% to be compounded monthly, the value of the investment after 10 years can be arrived at using the following steps –
P = 10000, R = 5/100 = 0.05, n = 12, Y = 10
If we load these figures in to the above formula, we get –
FV = 10000 (1 + 0.05 / 12) ^ (12(10)) = 16,470.09
So, the investment balance after 10 years is $16,470.09

YEAR YEAR’S INTEREST TOTAL INTEREST BALANCE
1
$511.62
$511.62
$10,511.62
2
$537.79
$1,049.41
$11,049.41
3
$565.31
$1,614.72
$11,614.72
4
$594.23
$2,208.95
$12,833.59
5
$624.63
$2,833.59
$12,833.59
6
$656.59
$3,490.18
$13490.18
7
$690.18
$4,180.36
14,905.85
8
$725.49
$4,905.85
$14,905.85
9
$762.61
$5,668.47
$15,668.47
10
$801.63
$6,470.09
$16,470.09

Positive Effects of Compounding

When Benjamin Franklin passed away in 1790, he bequeathed $5,000 each to the cities of Philadelphia and Boston. Both the cities were to build a fund that would last for 200 years. The needful were allowed to borrow at 5% interest. After 100 years, each of the cities could take out $500,000 from the fund, leaving the rest to grow over the subsequent 100 years. Why did Franklin do such a thing? His primary intention was to make people understand the positive effects of compounding.
Let’s look at 4 key benefits of compound interest:
  • Anyone Can Profit – You don’t need to be a Harvard Finance MBA to make compounding work for you. Any invested amount will earn you compound interest provided you leave it untouched.
Time is Your Best Friend – The longer you allow your money to compound, the quicker it will grow. A growth rate of 6% per annum will double your money in approximately 12 years, but will make it worth four times in 24 years.

Let Savings Compound As Often As Possible – When saving money, it is better if you compound quarterly rather than annually. $1,000, compounded annually at 10% will yield $1,470 in 5 years. $1,000, compounded quarterly at 10%, will fetch $1490 in 5 years.

Adds Up Faster Than You Think – If you were to save $50 a month for 10 years and earn 5% interest compounded each month, you would have accumulated $6,000 in savings. But the actual value of your saving would be $7,760. And, even if you decide not to add a single dime more, it would be worth over $15,000 in another 15 years.

Negative Effects of Compounding

Compounding is Dr. Jekyll in your investment account, but Mr. Hyde when it comes to credit cards. Let’s get in to some scary details. When you use your credit card to purchase something, the card issuer will charge you interest on the total amount you owe to the company. However, with time, the interest charged is not just applied on the principal, but also on the accumulated interest.
Let’s say you are sitting on a credit card debt of $5,000, which you plan to repay in 3 years. If the card issuer charges 12% interest, you would have dished out roughly $1,000 in interest payments by the time the loan is paid off. Now, if instead of the 3, you were to repay in 1 year, you would lose just $300 in interest charges. The reason? You are giving the credit card issuer much less time to let the magic of compounding work in its favour.

Compounding and Discounting in Finance

Compounding and discounting are two sides of the same coin. They are fundamental to the key economic concept of “time value of money.” Compounding enables you to estimate what a given amount of money’s worth will be in the future. Suppose you have $100 and can earn 4% annualized return. One year from now, you will have $100 multiplied by 1.04, or $104. In discounting, the opposite happens. You take an amount of money from a date in the future and translate it in to today’s value. Continuing from the above example, assume you can earn a yearly return of 4%. If you were to today save $96.15, you would generate exactly $100 one year from now. Thus, $100 in one year’s time is actually worth just $96.15 in today’s value. The following formula is used to discount a future cash flow to its present value:

Present Value = FV * (1+R) ^ (-n)

Where,

FV = Cash flow or the sum of money being converted
R = Average annualized rate of return
n = Number of years ahead

Final Thoughts

To sum up, one doesn’t need to be a serious numbers cruncher to demystify compounding. As an investor, compounding can be your passport to financial success. But as a borrower, it also has the power to skyrocket your debt.

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