If you don’t earn much and can barely pay your expenses, the idea of saving is ludicrous as just saving $30 or 1% of your monthly income may seem small and irrelevant. The old me would rather indulge in a good meal at Chomp Chomp than to save it in my piggy bank. Why would I even bother?

Because Rome wasn’t built in a day.

Everyone, including myself, has to start somewhere. Small pieces of bricks put together will eventually form a fortress. Our financial situation will improve over time and even the smallest amount of savings will definitely benefit us over the long run. This is largely due to the **power of compounding.**

Compounding is the process in which an asset’s earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will generate earnings from both its initial principal and the accumulated earnings from preceding periods. Compounding, therefore, differs from linear growth, where only the principal earns interest each period. -Investopedia

# The Math Behind Compounding

Power of compounding proves that time is our greatest asset when it comes to building wealth. Here’s the mathematical breakdown on a fixed deposit account.

For illustration purposes, let’s take $100,000 initial deposit with 5% annual interest and compare the differences between saving it for 5 to 40 years.

From the graph above, it’s shown that the 5-year growth increases with the number of years deposited, causing an exponential effect. This proves that the longer you let your money compound, the better. Which is why investors always like to say:

Time in the market is better than timing the market.

However, the above formula represents interest compounding at a continuous rate. Realistically speaking, interest doesn’t compound every day and second. A high interest savings account such as DBS multiplier compounds every month while an endowment plan offered by banks or insurance companies compounds 1-2 times a year. To put it into simple terms, the more times the interest money is **credited** annually, the better. A 2.5% interest savings account that credits twice a year is better than a 2.5% interest savings account that credits annually. So do remember this when you are considering two or more saving plans at similar interest rates!

## Effect of increased compounding periods per year

As you can see, having interest credited twice a year is definitely beneficial. Although the returns are small and negligible during the first few years, they could really ramp up over the long run and this difference would mean having an extra holiday with your family or not!

The actual formula for compounding is shown below:

**FV = PV * [1 + (i / n)] ^{(n * t)}**, where:

- FV = future value
- PV = present value
- i = the annual interest rate
- n = the number of compounding periods per year
- t = the number of years

# Case study

Now that you know compounding is basically earning interest on interests and time is our greatest friend, let’s take a look at a typical scenario.

Johnathan and Mike have the same retirement goal of wanting to retire at 65 with $1,000,000. They both, however, led very different lifestyles. Johnathan is a smart saver and started saving $500 every month since the age of 25. Mike led an active lifestyle and was willing to double Johnathan’s savings when he hit 40 to compensate the loss in savings during his mid-20s. They both put their money in a portfolio which compounds yearly with an average return of 7%. Let’s take a look at their retirement accounts at 65.

Annual addition | Years to grow | Interest rate | Compound |

$6,000 | Johnathan: 41 Mike: 26 | 7% | 1 time annually |

Total amount invested ($) | Final amount ($) | |

Mike | 312,000 | 881,806 |

Johnathan | 246,000 | 1,377,793 |

Difference | 66,000 | -495,988 |

% Difference | Mike invested 27% more | Mike had 35% less |

You must be wondering, how did Mike end up with 36% (496k) lesser than Johnathan despite saving 27% more? Ladies and gentlemen, this is the power of compounding! At 7% interest rate, taking the rule of 72, it takes roughly 10 years to double his capital. $6,000 would turn into $12,000, then $24,000 then $48,000 and finally $96,000 over 10, 20, 30 and 40 years. It was the final 1-2 doubles that really mattered and widened the gap between Johnathan and Mike.

## “I’ll start saving next year”

Sounds familiar? Although there is little harm by delaying a few years, we could miss out on great returns the later we start. Here’s the graph showing Johnathan’s returns should he start at ages 25, 26, 27, 28 and 29.

Age | 25 to 26 | 26 to 27 | 27 to 28 | 28 to 29 | Average |

Difference ($) | 96,136 | 89,847 | 83,969 | 78,476 | – |

Difference (%) | 93.02% | 92.99% | 92.95% | 92.92% | 92.97% |

On average, every year Johnathan delays reduces his potential returns by ~7%. Of course, this is not meant to scare any of you, but I hope these figures and graphs show you the importance of starting today. When people start to save, it often seems slow and pointless because things don’t change overnight. But as time passes, the rate of absolute change gets faster and faster and this is why the power of compounding is magical.

Before I finish, I would like to highlight that albeit the advantages of starting early, we should’t have a one-track mind and only focus on growing our wealth. If you’re like me and enjoy spending on movies, concerts and cafes, you don’t have to overly sacrifice your lifestyle just to lead the ‘suffer now, enjoy later’ life. Remember, progress is best made in a moderate and sustainable manner.

The future is unpredictable, so we should find a good balance between saving and spending. The best way is to set a goal and live within our budgets. I’ve covered this in my previous article: *The Newbie’s Guide to Budgeting.*

Lastly, if you don’t know how to find consistent returns on your savings and investments, my suggestion is to talk to your trusted financial adviser. I’m a huge fan of diversification and although I prefer to manage my own portfolio, I also feel the need to allocate a portion of my savings in a high growth investment plan. This protects me from the risk of losing all my savings if my investments were to turn ugly. If you are looking for an agent that comes from an investment banking background and managed to bring consistent returns for his clients, you may contact me at *thefivelayers@gmail.com* and I’ll link you up with him. Thank you for reading and happy building your layers.

The video below summarizes this article in two minutes.

*Featured image from Business insider