# 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.”