Lesson

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

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.