# Compound Interest – A Real 8th Wonder!

“Compound interest is the eighth wonder of the world. He, who understands it, earns it…he who doesn’t….pays it.”

– Albert Einstein

Surprised! Let me take you through below article & you will know why compound interest is called as the 8^{th} wonder of the world.

To understand compounding let just start with **simple interest** that is calculated only on the principal amount. For example, you put Rs.1000 into a bank account. How much will your deposit be worth in 1 year at an annual interest rate of 7.5%? The answer is Rs.1075, and your earned interest is Rs.75.

In the case of **compound interest,** the principal in each time of period is different. The bank won’t give the earned interest back to you; instead of that, they will add it to your principle amount. This increased amount becomes the principal for the next period (called as compounding period) and also earns interest. Putting in simple words, you earn interest not only on the principal amount but also on the interest earned in each compounding period.

In our example, in addition to the principle amount of Rs.1000, the earned interest of Rs.75 will also earn interest next year. So, how much will your Rs.1000 deposit be worth after 2 years at the annual interest rate of 7.5%? The answer is Rs.1156, and you can calculate it in several ways, as demonstrated below.

**Comparison of Simple Interest Vs. Compound Interest –**

Let’s say you have Rs.1000 in your account & you invest them at 8.5%.

From above chart, you can see that if you invest Rs.1000 per year for 40 years at the interest rate of 8.5% by the compound interest, you can get Rs.26,133, whereas by simple interest method you will only get Rs.4,400.

**The Benefits of An Early Start –**

In most financial planning models, money saved between ages 25-35 produces more money than all savings between 35-60!. Ready to get wondered? Let’s assume you have X amount in your account. Now see what can be your compounding interest after each 10 years.

As you can see here, the value of your Rs. 1000 will be Rs.2,261 after 10 years, Rs.5,112 after 20 years, Rs.11,558 after 30 years, etc. This is called as Power of Compounding.

**Starting Early is the Secret to become Wealthy –**

Let’s look at an example to show how saving early can positively affect your investment balances. Investor A decides to start saving at the age 25. He saves Rs.1000 a month in his saving account until age 35. At this point, he stops saving and just let’s interest work in his favor. At age 60, assuming a 7.5% annual rate of return he will receive Rs.11.53 lakhs even though he only contributed Rs.1.20 lakhs total into his account.

Investor B decides to wait until he is 35 to start saving. He saves the same Rs.1000 a month that Investor A did but he actually saves that amount right up until the age of 60. His total amount contributed to his account over those 25 years would be Rs.3.60 lakhs. Assuming he also earns an annual return of 7.5% on his funds he will end up with Rs.8.77 lakhs when he reaches 60. Let’s see exact details as below.

Even though Investor B contributed 3x as much money as Investor A did, he actually ends up with almost Rs.2.76 lakhs less than his at 60. The reason for this is compound interest. Compound interest means that you earn interest initially on your principle balance and then continue to earn interest on the peak of your interest which snowballs until you have a runaway freight train working in your favor.

Let’s assume Investor A doesn’t stop saving at age 35. Instead, he continues saving the same amount his entire career until he retires at age 60. With the same assumptions, he now has over Rs.20.30 lakhs at retirement. His 10-year head starts on Investor B gave him more than 2 fold his closing balance. Again this is compound interest helping his cause.

All is not lost if you have not started saving yet. You will just have to make up for your shortfall in years by increasing the amount you save. If you start at age 35 (same assumed 7.5% return) and save Rs.1500 a month, you can still retire at age 60 with Rs.13.15 lakhs. Your increased contributions can make up for some of the lost time.

**Compounding frequency –**

Compounding can be done on a daily, monthly, quarterly, half-yearly or annual basis. Shorter the interval of compounding, greater the impact.

**General formula to Calculate Compound Interest –**

PV – Present value of the investment

i – Interest rate earned per year

n – Number of years

By knowing these elements, you can use the following formula to obtain out the future value of the investment with a particular compounded interest rate:

**F V = PV * (1 + i) ^{n}**

Let’s take an example & see how compounding frequency matters in the long term. Assume that PV = Rs.1,000, i = 8.5% & n = 10.

In the case of general i.e. **Annual** compounding above formula will be applicable. Here we will get Rs.2,261

FV = Rs,1,000 * (1+0.085)** ^{10 }**= Rs.2,261

In case of **Monthly** Compounding,

i = 8.5% per year, compounded monthly (0.085/12) & n = 10 years x 12 months (10*12=120)

Input above numbers in the formula, and you will get:

= Rs.1,000 * (1 + 0.85/12)^{10×12 }= Rs.2,333

Similarly, you can also calculate **Daily** compound interest by below formula.

i = 8% per year, compounded daily (0.085/365)

n = 10 years x 365 days (10*365 =3650)

Input above numbers into the compound interest formula and you will get the following result:

=Rs.1,000 * (1 + 0.085/365)^{10×365} = Rs.2,339

See: –Compound Interest Formula and Excel Calculator

## Summary –

Compounding interest is the real 8^{th} wonder of the world. In order to get benefits from it

- Start Investing as early as possible & Stay invested for longer term
- Keep compounding interval short. Shorter the compounding interval, the greater the benefits you will get.