*Would you care to guess?*

- How much do savings of Rs. 10,000/- per month &/or weekly expenses of Rs. 500/-, affect your wealth creation over your working life (say 30 years)?
- How deeply is your post-retirement life shaped by wealth that you create in early stages of working life?

*Ever wonder?*

- Why don’t people with same financial resources & opportunities, end up with same wealth outcome?
- Why do certain people get rich while others don’t?

Luck may have a little bit to do with all above, being at a right place at the right time too but that is only a little bit. It certainly has a lot to do with what Einstein called the eighth wonder of the world – the compounding concept.

*Compounding is the process of generating income on an asset’s reinvested earnings.*

- Simple interest is applied only to the principal & not any accumulated interest.
- Compound interest is interest accruing on the principal & previously applied interest.
- The effect of compound interest depends on how frequently it is applied.

It represents an investment’s progress over period of investment, assuming return is re-invested each year in the scenario of volatile annual growth. Compounded Return takes into account both ** rate of return **&

**for which money remains invested. The compound interest formula is:**

*time**A = P (1 + r/n) ^{nt}*

**A **= Future value of your investment,

**P = **Principal (the amount of money you start with);

**R **= Annual nominal interest rate before compounding;

**T **= Time (in years) &

**N =** Number of compounding periods in each year (365 for daily, 12 for monthly, etc.)

COMPOUNDING @ 12% per annum | |||||

Year | Year Opening Balance (Rs.) | Yearly Return (Rs.) | Total Compounded Return (Rs.) | Compounding Effect (Rs.) | Closing Balance (Rs.) |

(A) | (B) | (C=B*12%) | (D = FV-PV) | (D – 12*A) | (FV) |

1 | 100.00 | 12.00 | 12.00 | 0.00 | 112.00 |

2 | 112.00 | 13.44 | 25.44 | 1.44 | 125.44 |

3 | 125.44 | 15.05 | 40.49 | 4.49 | 140.49 |

4 | 140.49 | 16.86 | 57.35 | 9.35 | 157.35 |

5 | 157.35 | 18.88 | 76.23 | 16.23 | 176.23 |

10 | 277.31 | 33.27 | 210.58 | 90.58 | 310.58 |

15 | 488.71 | 58.64 | 447.36 | 267.36 | 547.36 |

20 | 861.28 | 103.35 | 864.63 | 624.63 | 964.63 |

25 | 1517.86 | 182.14 | 1600.01 | 1300.01 | 1700.01 |

30 | 2674.99 | 321.00 | 2895.99 | 2535.99 | 2995.99 |

In the illustration above, compounding @12% p.a. on investment of Rs. 100/-, return in in fifth year Rs. 18.88 & in the 10th year is Rs. 33.27. In the 5-year subsequent gaps, return for that year goes up to 58.64, 103.35, 182.14, 321.00 & so on.

- The yearly return is
*not increasing at constant rate*but exponentially & *Exponential growth*is due to the fact that pile of*return on ‘total return of previous periods’*, keeps getting bigger with passage of time. As a result, return in each time period grows at a faster pace than previous period, driving rate of growth of return in ever-increasing spiral.

* Rule of 69 – *Rule of 69 is an estimation of

*amount of time required for an investment to double*, assuming continuously compounded interest.

*T = [(69 / R) + 0.35]*

T = Number of Periods required to double an investment’s value

R = Continuously Compounded Interest Rate per period, as a percentage

To estimate the time, in which a bank FD @ 5.25% p.a. of Rs. 1 lakh will increase in value to Rs. 2 lakhs >>> T = [(69 / 5.25) + 0.35] = 13.49 years.

*Compounding has a lifelong impact*

* Positive impact* – Every additional rupee saved & invested, every rupee in tax saved / postponed on account of tax planning – makes us wealthier due to additional return on returns already earned. Improving rate of return on investment, directly contributes to the pace at which compounding happens.

** Negative impact **– Compounding is a mathematical phenomenon & works on costs just as it does on returns. Unsustainable costs destroy wealth & negative impact of such cost too accumulates at exponential rate, with passage of time. The effect on wealth is

*visible in cash costs*such as interest payable on debt,*camouflaged in hidden costs*such as loss of purchasing power (due to inflation)*hidden in plain sight*in cases when legitimate means to reduce expense & tax outgo are not adopted, leading to loss of opportunity for higher savings.

* Periodicity of compounding* – Effective Annual Rate (EAR) is critically relevant factor in bank financing options & loans. It signifies the effective annual interest rate on debt after taking into account, number of times interest cost is compounded during the year. Most common applications are in overdraft & home loans. For example, interest on overdraft account is debited each month.

- An OD interest rate (12%) that you think that you are paying is actually 12.68%.
- On an overdraft of Rs. 100, it is an additional Rs. 0.68 in first year but accumulates to extra Rs. 598.97 over 30 years.

*Compounding in Real Life*

Investment proposals with dissimilar principal amount & time horizon are compared on common factor of Compounded Annual Growth Rate (CAGR).**Alternate investment proposals**–

While a case can be made for incurring debt to create productive asset, incurring**Credit Card Debt**–*debt to maintain lifestyle*compounds the negatives of higher interest rate & reduced savings for investment.

‘Additional Savings’ required in the time left for financial goal, to bridge the deficit between the financial goal & corpus accumulated thus far, can be calculated using the compounded return formula.**Investment Gap**–

COMPOUNDING @ 12% per annum | ||||

Principal | Future Value (Rs.) | Accumulated Return (Rs.) | Period of investment (Years) | Additional Time Taken (Rs.) |

100 | 200 | 100 | 6.12 | 6.12 |

100 | 300 | 200 | 9.69 | 3.57 |

100 | 400 | 300 | 12.23 | 2.54 |

100 | 500 | 400 | 14.20 | 1.97 |

100 | 600 | 500 | 15.82 | 1.62 |

It is a significant stage in personal finances when ‘accumulated returns’ starts adding as much gains as ‘principal investment’ would. Beyond such stage, trajectory of wealth accumulation becomes steep. In the illustration above, wealth becomes 2X of the principal amount in 6.12 years & 3X by 9.69 years but it needs just another 6.13 years to become 6X. In other words, time needed to progressively increase wealth – by an amount that is equal to original investment – reduces at exponential rate.**Transformative Power of Compounding**–

– It reflects the loss of value on account of time. Time is more important to the outcome of an investment than the rate of return because an investor has some control over time to be given to an investment, unlike rate of return that is dependent on investing environment. Any reduction in one of the two factors – rate of return & time – necessarily increases the need for other. Procrastination is a common human failing, therefore shortening the time span of investment translates into higher need for savings to achieve financial goal. In case of financial goal with undefined time horizon, cost of delay is loss of opportunity to create additional wealth. Cost of delay is the leakage of value.**Cost of Delay in Investing**

David Bach emphasized the importance of**Latte Factor**–*repetitive discretionary expenses however small*, in wealth creation outcome over a period of time. It draws attention to expenses done as a matter of habit but which are unnecessary or do not provide commensurate satisfaction/happiness. These could be coffee, beer, subscriptions, weekend parties etc. He pointed out that isolated small value wasteful expenditures, if combined,*are a source of additional investment & great potential value*. The value of course, is embedded in exponential power of compounding & time value.

Particulars | Reference | Investor A | Investor B |

Annual Rate of Return | | 12% | 8% |

Period (years) | | 30 | 20 |

SAVINGS | |||

Annual Investment (Rs.) | | 120,000 | 120,000 |

Total Investment | (i) | 3,600,000 | 2,400,000 |

Total Value at end of period (Rs.) | (ii) | 28,959,922 | 5,491,436 |

Growth (ii -i) | (iii) | 25,359,922 | 3,091,436 |

Cost of Procrastination & Inferior Return (Investor B) (iii A – iii B) | (iv) | – | 22,268,486 |

EXPENDITURE | |||

Discretionary & Avoidable Weekly Expense (Rs.) | | 500 | 0 |

Reduction in Cash Outgo over 30 Years (Rs.) (500*52*30) | (v) | 780,000 | 0 |

Future Value of Discretionary Expenses @ 12% p.a. (Rs.) | (vi) | 7,697,854 | 0 |

Loss of Opportunity for Investor B (Rs.) | (vii) | – | 7,697,854 |

DOUBLE FAULT <<< >>> Saving less & Spending more | |||

Total Savings Invested (Rs.) (i + v) | (viii) | 4,380,000 | 2,400,000 |

Total Wealth Creation (Rs.) (ii + vi) | (ix) | 36,657,777 | 5,491,436 |

Extra Wealth Creation by Investor A (Rs.) (ix A – ix B) | (x) | 31,166,341 | |

Cost of Poor Investment Choices by Investor B (iv B + vii B) | (xi) | | 29,966,341 |

**Playing the Long Game**

Most people play the *short game* of going for the most visible & immediate benefit. Anything that is hard is put off for another day. However, it is important to invest in success every single day. The daily effort yields tiny advantages that accumulate & over time become a foundation for more & better results. This is the *long game* that compounds rewards in life.

Every decision in life is a move towards either short or long game. Time amplifies whatever good or bad that comes of these decisions. Such an understanding can be applied to all things that matter in life.

*Compound Knowledge** – to fast track your progress in profession / business by contributing more value in least time.*

*Compound Relationships** – to love & feel loved, to enrich life of people around you, to lead a happy & balanced life.*

*Compound Financial Returns** – to create wealth & achieve financial freedom*

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