A legendary historical figure, Albert Einstein is well-known to all generations.

His wild hair and bushy mustache are easily recognizable even to young children from photos.

But Einstein's influence goes far beyond his distinctive appearance.

Einstein was an exceptional mathematician and scientist. His contributions to the theory of relativity fundamentally changed how we think about space, time, and gravity.

However, his genius extended beyond physics.

Einstein may have had unique insights into banking, particularly compound interest, due to his aptitude for numbers and patterns.

In addition, he had a talent for demystifying difficult ideas so that everyone could grasp them.

## Einstein and compound interest

His theories on compound interest can teach us important financial lessons.

So he said the most popular compound interest quote:

“Compound Interest is the eighth wonder of the world, he who understands it, earns it; he who doesn't, ...pays for it.” - Albert Einstein

This quote emphasizes the idea that by simply investing your money and allowing it to compound, you can significantly increase your wealth, making it seem almost magical.

So understand compounding interest is a must for investment.

The key factor that makes compound interest so powerful is time.

The longer you leave your money to compound, the more substantial the growth and enhances your personal finance.

This is why compound interest is particularly beneficial for long-term investments, such as retirement savings.

Compound interest is different from simple interest as it is an interest earned on interest.

Simple interest is a fixed rate over time, based on the initial amount you’ve invested.

## MATHEMATICAL PROOF

### Simple Interest

To understand simple interest, let’s assume you deposit $100 into an account with a 5 percent interest rate.

Multiply your principal by the interest rate, and then the amount of time you expect to keep that money in the account.

One hundred dollars times 5 percent, or 0.05, is $5.

Keep that account going for 50 years, and you’ll earn $250 in interest, for a grand total of $350.

```
P = 100, r =5%, t = 50 years
Simple Interest = (P x r x t)
100 x 5% = 5
5 x 50 = 250
```

### What is Compound Interest

Compound interest is different.

It’s interest on top of interest.

If you use it correctly, you can turn small initial investments into small fortunes by significantly enhance the growth of your investment portfolio.

Thats why its a common saying power of putting your money to work by earning interest.

By __leveraging__ the concept of compounding, you can harness the potential of your investments and generate substantial wealth over time.

The beauty of compounding lies in its ability to create a snowball effect, where your initial investment gains momentum and multiplies exponentially.

Imagine a scenario where your investment not only earns returns on the principal amount but also generates additional returns on those returns.

This compounding effect can unlock extraordinary growth opportunities that may seem unattainable otherwise.

By embracing compounding, you can accelerate your journey toward financial freedom and achieve your long-term financial goals.

## 4 TYPES OF COMPOUND INTEREST

Let’s take that same $100 from the first example, and the same 5 percent interest rate.

If that interest rate compounds each year, your $100 would turn into $1,146 at the end of 50 years.

If you matched your initial investment of $100 each month, without changing anything, you’d end up with $252,132 after 50 years.

**TECHNICAL CALCULATIONS (ADVANCED MATHEMATICS)**
P = 100/- amount, r =5% rate, t = 50 years, n=12 periods
WITHOUT CONTRIBUTION
**1-Compound Interest = P x (1+r/100)^t (Annual)**
(1 + 5/100) = 1.05
1.05 ^ 50 = 11.467
100 x 11.467 = 1,146 (Annual Compound Interest at the end of 50th year)
**2-Compound Interest = P x (1+[r/100]/n)^(t*n) (Periodic)**
(1 + 0.05/12) = 1.00417
50 x 12 = 600
1.00417 ^ 600 = 12.143
100 x 12.071 = 1,214 (Periodic Compound Interest at the end of 50th year)
From here, it become 8th wonder of the world
WITH CONTRIBUTION (Regular Payments i.e. Annuity)
**3-Compound Interest = P x (1+[r/100]/n)^t (Annual + Contribution)**
(1 + 5/100) = 1.05
100 x 11.467 = 1,146 A
100 x (11.467-1)/0.00417 = 251,007 B
A + B = 252,132
**4-Compound Interest = P x (1+[r/100]/n)^(t*n) (Periodic + Contribution)**
(1 + 0.05/12) = 1.00417
50 x 12 = 600
1.00417 ^ 600 = 12.143
100 x 12.143 = 1,214 A
100 x (12.143-1)/0.00417 = 267,218 B
A + B = 268,432

## COMPARSION OF PRINCIPAL SIMPLE AND COMPOUNT INTEREST (INTEREST CALCULATOR)

```
TECHNICAL CALCULATION OF ABOVE
P = 6,000/-, r =7% rate, t = 40 years, n=1 annual period
WITHOUT CONTRIBUTION
1-Compound Interest = P x (1+r/100)^t (Annual)
(1 + 7/100) = 1.07
1.05 ^ 40 = 14.974 approx. 15
6,000 x 15 = 90,000/- (Annual Compound Interest at the end of 40th year)
```

### Interest Calculator

*Verify the calculation by yourself **https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator** (above calculations are manual different from this calculator due to rounding differences)*

Compound interest can be great for investing your money, but if you are looking for a loan, it could easily let your debt grow out of control specially credit card debt.

The same compound interest used to make your investments grow __exponentially over time__, can also be applied to your unpaid balance on certain loans. This is we can see in the Insurance Market and Stock Market

That’s why it is famously being said that compound interest 8th wonder of the world.

Also, another finance genius said about compound interest.

"My wealth has come from a combination of living in America, some lucky genes, and compound interest." - Warren Buffett

Hence it is proved that compound interest is the 8th wonder of the world.

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