# Simple VS Compound

Lesson

Now that we've had a good look at both simple interest and compound interest, let's compare them side by side.

##### example

Let's say we have $\$10000$$10000 to invest and we have two options. Option 1: Invest at 5%5% per annum simple interest Option 2: Invest at 4.5%4.5% per annum compound interest, compounded annually At first glance it appears that the higher interest rate in Option 1 would naturally be the better choice, but let's see what happens. Year Simple Interest Compound Interest Simple Interest Balance Compound Interest Balance 11 500500 450450 1050010500 1045010450 22 500500 470.25470.25 1100011000 10920.2510920.25 33 500500 491.41491.41 1150011500 11411.6611411.66 44 500500 513.52513.52 1200012000 11925.1811925.18 55 500500 536.63536.63 1250012500 12641.8112641.81 66 500500 560.78560.78 1300013000 13022.5913022.59 We can see that the interest remains constant each year for simple interest but due to the nature of compounding, the interest is increasing each year. At the 6 year mark, the balance for the compound interest option yields a greater return. Let's look at the same situation, but this time let's look at what happens if Option 2 was compounded monthly. Simple Interest Balance after 6 years: \13000$$13000

Compound Interest Balance after 6 years, compounded annually: $\$13022.59$$13022.59 Compound Interest Balance after 6 years, compounded monthly: 10000\left(1+\frac{4.5}{100\times12}\right)^{\left(12\times6\right)}10000(1+4.5100×12)(12×6)=\13093.03$$13093.03

We can see here that the more often the investment is compounded, the greater the amount of interest accrued.