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# COMPOUND INTEREST - Why its 8th Wonder of the World

Updated: Sep 10

Compound interest — it’s either the easiest way to double or even triple your savings, or a sure-fire ticket to bankruptcy.

Compound interest is different from simple interest. Simple interest is a fixed rate over time, based on the initial amount you’ve invested. Image by Author - Eighth Wonder of the World

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```

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.

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 \$252,364 after 50 years.

```P = 100, r =5% , t = 50 years

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

2-Compound Interest =  P x (1+[r/100]/n)^(t*n) (Periodic)
(1 + 0.05/12) = 1.00416
50 x 12 = 600
1.00416 ^ 600 = 12.071
100 x 12.071 = 1,200

From here, it become 8th wonder of the world

3-Compound Interest =  P x (1+[r/100]/n)^(t*n)(Annual + Contribution)
(1 + 5/100) = 1.05
100 x 11.467 = 1,146 10.921
100 x (11.467-1)/0.00416 = 251,610
A + B = 252,756

4-Compound Interest =  P x (1+[r/100]/n)^(t*n)(Periodic+Contribution)
(1 + 0.05/12) = 1.00416
50 x 12 = 600
1.00416 ^ 600 = 12.071
100 x 12.071 = 1,200 A
100 x (12.071-1)/0.00416 = 266,129 B
A + B = 267,329```
###### 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. The same compound interest used to make your investments grow exponentially over time, can also be applied to your unpaid balance on certain loans.

That’s why it is famously being said:

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