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Compound Interest


wealthymatters.comWe all pick up some pretty important stuff in primary school but it’s doubtful if we really appreciate their importance at the time.Compound interest is one such thing.For many people  it’s a formula to be memorized to pass a few math tests only to be forgotten or at least be pushed back to the recesses of their minds along with all the rest of the facts memorized in childhood.

To refresh memories, compound interest is the type of interest calculation where periodic interests accrued are not paid out but retained and the accrued interests earns interest . The formula for calculating compound interest is:

A = P\left(1 + \frac{r}{n}\right)^{nt}

Where,

  • A = final amount
  • P = principal amount (initial investment)
  • r = annual nominal interest rate (as a decimal)
  • n = number of times the interest is compounded per year
  • t = number of years

The formula must evoke memories of doing sums as children,where we read the problem,identified the values of  the various given variables,value substituted in the formula and solved for the unknown value.For all those who no longer want to test their mental math skills, here is a link to a calculator that helps us solve for principal,rate,time and amount http://www.1728.com/compint.htm So, for a bank or company fixed deposit or government or corporate bond a we can figure out the amount we will have at the end of the tenure by using this calculator to solve for amount.In case of a zero coupon bonds we can figure out the rate of interest being offered by keying in the principal,amount and tenure.If we are saving up for something and have a target sum in mind and are contemplating various investment products with different initial investments , rates and compounding frequencies , we can compare them by using the calculator to solve for time , to check how soon we can have what we want and we need to do to get there.

Also the formula and above calculator can be used to evaluate the perfomance of investment porfolios, individual stocks , mutual fund and ETF , bullion, real estate, business and alternative  investments by figuring out the compounded annual growth rates and comparing them to various benchmarks.This exercise helps us figure out how well our investments have done vis-a-vis the average investment in the class.By comparing actual returns from various investments  across  asset classes we can decide how many of our investments are worth the risks and hassles of owning them.For more on this click on this link : https://wealthymatters.com/2011/01/26/cagr-calculator/

The compound interest formula is however more than just a nifty tool to handle investments.Grasping the math behind it,offers profound insights into wealth building.It can show us how small or seemingly insignificant actions can lead to the build up of massive family fortunes.

In

 A = P\left(1 + \frac{r}{n}\right)^{nt}

Its easy to see  Amount depends on Principal,rate of interest,the frequency of compounding(n) and the time.Of these variables the most significant is is the combination of nxt in the exponent.To get an idea of how important n is we can keep P , r and compound frequency constant and run the numbers using the above calculator.We get the following table and the multiple figure shows how many times the Principal has grown over the years.

Time – n  10 20 30 40 50 60 70 80 90 100
Principal – P 100 100 100 100 100 100 100 100 100 100
Rate of Interest – r 10 10 10 10 10 10 10 10 10 10
Amount – A 259.37 672.75 1744.94 4525.93 11739.09 30448.16 78974.7 204840 531302.3 1378061
Multiple 2.6 6.7 17.4 45.2 117.4 304.5 789.7 2048.4 5313 13780

This result has many practical implications.For one, in the case of saving for retirement . Following is an example  from a book called “The Random Walk Guide to Investing ‘ by Burton Malkiel.

William and James are twin brothers who are 65 years old. 45 years ago (at the end of the year when he reached 20), William started an IRA and put $2K in the account at the end of each year. After 20 years of contributions, William stopped making new deposits but left the accumulated contributions in the IRA fund. The fund produced returns of 10% per year tax-free. James started his own IRA when he reached the age of 40 (just after William quit) and contributed $2K per year for 25 years, making his last contribution today. James invested 25% more money in total than William. James also earned 10% on his investments tax-free. What are the values of William’s and James’s IRA funds today?William has $1,365,227. James has $218,364. James invested 25% more than William, but through the magic of compounded returns, William’s IRA fund is worth more than six times as much!

The same principle applies if you are saving for youe children’s education etc.In fact if you are serious about making your family wealthy why not start investing small sums of money in your children’s names right after they are born ?Why not get the child a piggy bank and teach them to save up small cash.You could also teach them not to dip into the piggy-bank for day to day needs.This should teach them delayed gratification,which is so important to building wealth. Then you could take them along to the bank and show them how to make deposits.Maybe you could get them to deposit any prize money they win and a part of  the money they make from doing chores  into the account .Going to the bank might be an occassion to discuss investing,interest rates,risk etc.Their small savings are likely to grow to a respectable sum by the time they reach majority and by then they would be disciplined savers and canny investors too.

wealthymatters.com

The above graph illusterates how money grows exponentially as the tenure of investments increase.In fact the gains are startling in the final part of the tenure.Now waiting for a 100 years or more is not practical for one person,but if 3-4 generations of a family work at getting wealthy,it’s a lot easier to use the power of compounding .In fact here is an example of how cities benefitted from compounding http://www.crackerjackgreenback.com/the-basics/compound-interest-a-lesson-from-benjamin-franklin/

To repeat, time is the most important factor in building  wealth.Arguments, about how inflation and taxes make it impossible for people to grow wealthy by compounding their money, stem from a limited understanding of compound interest itself.Compound interest doesn’t just apply to paper assets like bonds.There are always asset classes that are not adversely affected by inflation and there are always tax-exempt avenues for investment.Moreover, when wealth is dispersed in a family the incidence of taxation on wealth is bound to be lower.Wealth building is not just about number crunching using the compound interest formula,but about imaginatively and skillfully applying the principles condensed in the formula.Money making is as much or more a right brain activity than a left brain one.

Aside from time which makes a huge difference in wealth,over longer periods,the frequency of compounding also produces marked gains as shown in the table below.So in the case of term deposits and bonds,where the rates and tenure are the same,it makes sense to pick the one which compounds oftener. In case of non-paper assets this means we should pick up the assets that pay us back faster at shorter intervals.For example, businesses where the owner gets paid upfront or where debts can be collected faster.

Frequency of Compounding Annual Semi-Annual Quarterly Monthly Daily Continuously
Principal – P 100 100 100 100 100 100
Time – n 100 100 100 100 100 100
Rate of interest – r 10 10 10 10 10 10
Amount – A 1378061.23 1729258.08 1947808.05 2113241.46 2199631.87 2202646.58

 Rate of interest makes the next big difference to returns as seen in the table below:

Rate of interest – r 5 8 10 16 21
Principal – P 100 100 100 100 100
Time – n 100 100 100 100 100
Amount 13150.13 219976.13 1378061.23 279125119.9 18990527646

 The table may make you want to chase returns. That can be dangerous.Unless you know what you are doing and have a greater deal of control over results you run the risk of losing everything.20%, 40%, 60% returns in the first years are great, but if there is a -80%, -90%, or -100% in there anywhere, it’s game over because you will have lost your capital and need to accumulate it again.Benjamin Graham was aware of this risk when he said that more money has been lost reaching for a little extra return or yield than has been lost to speculating. Better slow and steady rather than fast furious and dead.

The least important variable is the original principal as seen from the table below.Double the principal just gives double the amount for any period.The moral of the story?It doesn’t matter if you start small.It’s more important to start and don’t let anyone else’s opinion stop you.A little goes a long way over time.

Principal – P 100 200
Time – n 100 100
Rate of interest – r 10 10
Amount 1378061.23 2756122.47

Following are a few calculators based on the Compound Interest formula.We can use the one above to do everything these can.I just added them for the graphic illustrations they produce.

http://economictimes.indiatimes.com/personal-finance/calculators/retirement-savings-calculator-/right-sum-to-retire-with/calculator_show/6706882.cms  ——to calculate retirement savings

http://economictimes.indiatimes.com/personal-finance/calculators/final-worth-of-investment/your-investment-ticker/calculator_show/6707009.cms ——– to calculate returns from  fixed return instruments

http://economictimes.indiatimes.com/personal-finance/calculators/saving-target-calculator/way-to-being-a-crorepati/calculator_show/6706977.cms  ——– for savings goal setting and monitoring

Here is a way of mentally calculating the rate of interest or term of doubling,tripling,quadrupling etc. https://wealthymatters.com/2011/01/26/rule-of-72-rule-of-70-rule-of-69/

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About Keerthika Singaravel
Engineer,Investor,Businessperson

24 Responses to Compound Interest

  1. anna says:

    Hello! This is my 1st comment here so I just wanted to give a quick shout out and tell you I truly enjoy reading your posts.

    Can you suggest any other blogs/websites/forums that deal with the same subjects? Thank you so much!

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  3. Cleta Havir says:

    Interesting article. I enjoyed it very much! Thanks. Cleta Havir

  4. Did you design the site this well with the default blog tools? Your blog is incredible.

  5. Alberta says:

    Some lecture!But a pretty detailed treatment of the subject I dare say!

  6. Doloris Schreur says:

    Very helpful information.Thank you.

  7. Penny Crissey says:

    Amazing thing Compound Interest! Very helpful info. Thanks.

  8. Misha Balder says:

    Nice piece.

  9. Ethelyn Lam says:

    Interesting information.

  10. Adolfo Haisley says:

    Just the sort of write-up I was looking for ,for a very long time.

  11. Misha Balder says:

    Nice article.Very useful information.Thank you.

  12. Ernie Symore says:

    Great post.Thanks.

  13. Millard Yuasa says:

    Excellent explanation.

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