# The Art of Compound Interest

By Arjun Chandrasekar.

Summary

Known as the 8th wonder of the world, compound interest is simply a formula used to calculate the interest on interest. It’s the result of reinvesting the interest made from an asset, accumulating even more earnings during the next cycle. Through time this formula exponentially enhances the frequency of compounding periods,  resulting in greater interest yields. This is why financial experts highly recommend that you start saving money early in your life, and continuously deposit as much money as you can, and if all goes well you’ll have more money than you need by the time you retire.

Simple vs Compound Interest

In order to understand compound interest we need to first understand simple interest. Simple interest is calculated by the formula: A = P(1 + rt), where A = final amount, P = principal amount, r = annual interest rate, and t = time (usually in years). It’s calculated based on the initial deposit, and is usually used for loans, mortgages, etc.

Compound interest on the other hand is calculated by the formula: A = P(1 + r/n)nt, where A = final amount, P = principal balance, r = interest rate, n = # of times the interest is applied in the given time period, and t = number of time periods.

Let’s try an example so it’s easier to notice the difference. Let’s say that you’re looking to buy a car and want to take out a loan for \$5,000 at an interest rate of 5% for the next 5 years. We can easily calculate this by plugging in the values into the formulas above.

Simple Interest: A = 5000(1 + 0.05(5)) = \$6250

Compound Interest: A = 5000(1 + 0.05/1)^5 = \$6380

Based on our final amounts, through simple interest, you’d have to pay approximately \$130 less than with compound interest. Compound interest, however, can work in your favor. When you go to keep savings in banks, they pay the compound interest daily, allowing you to benefit with a great interest rate for a long period of time. This is what experts mean when they say “make your money work for you.”

Now let’s look at an example of only compound interest, but for different periods of time. Based on the formula, you can tell that the time period variable is the exponent, so compounding your money for longer periods of time will allow for a larger exponential growth.

Let’s say you save \$2000 every year from the age of 18  until the age of 50. You keep your money in a savings account with a 6% interest rate. If you plug the values into the formula, you get a final amount of approximately \$195000. However, if you start a bit later at the age of 25 and save until 50, the final amount is approximately \$118300. That’s about \$76700 you missed out on! So start as early as possible, even if it’s only a little bit of money at first.

Conclusion

Understanding and utilizing the art of compound interest from an early age can immensely benefit your personal finances. Even if you’re still in school, ask your parents to create a credit card and/or a savings account in your name, so you can start depositing whatever money you have immediately.