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$$10000 to invest and we have two options.
Option 1: Invest at $5%$5% per annum simple interest
Option 2: Invest at $4.5%$4.5% per annum compound interest, compounded annually
At first glance it appears that the higher interest rate in Option 1 would naturally be the better choice, but let's see what happens.
| Year | Simple Interest | Compound Interest | Simple Interest Balance | Compound Interest Balance |
|---|---|---|---|---|
| $1$1 | $500$500 | $450$450 | $10500$10500 | $10450$10450 |
| $2$2 | $500$500 | $470.25$470.25 | $11000$11000 | $10920.25$10920.25 |
| $3$3 | $500$500 | $491.41$491.41 | $11500$11500 | $11411.66$11411.66 |
| $4$4 | $500$500 | $513.52$513.52 | $12000$12000 | $11925.18$11925.18 |
| $5$5 | $500$500 | $536.63$536.63 | $12500$12500 | $12641.81$12641.81 |
| $6$6 | $500$500 | $560.78$560.78 | $13000$13000 | $13022.59$13022.59 |
We can see that the interest remains constant each year for simple interest but due to the nature of compounding, the interest is increasing each year. At the 6 year mark, the balance for the compound interest option yields a greater return.
Let's look at the same situation, but this time let's look at what happens if Option 2 was compounded monthly.
Simple Interest Balance after 6 years: $\$13000$$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.