Simple vs. Compound Interest

Interest is a concept you come across every day, even if you don't realize it. It has to do with the money you save or borrow. It's like a reward for saving money and a cost for borrowing money. There are two popular types of interest that people talk about: simple interest and compound interest. Let's understand what they mean and how they work with easy examples and visualizations.

What is simple interest?

Simple interest is called "simple" because the way it is calculated is straightforward. When you save or borrow money, interest is calculated on the original amount you saved or borrowed. This amount is called the "principal."

Simple interest formula

Simple Interest (SI) = Principal (P) × Rate of Interest (r) × Time (t)

Here's how to find each part of the formula:

• Principal (P): The initial amount of money saved or borrowed.
• Interest rate (R): The percentage of interest you earn or pay, usually per year. It is often written as a percentage.
• Time (T): How long the money is saved or borrowed, usually in years.

When you multiply these two together, you get simple interest. It tells you how much extra money you will have to pay back if you borrowed money or how much you will get if you saved money.

Example of simple interest

Let’s say you have $100 and you deposit it in a bank account with an interest rate of 5% per annum for 3 years.

Principal (P) = $100
Rate of interest (R) = 5% per annum = 0.05
Time (T) = 3 years

Simple interest (SI) = 100 × 0.05 × 3 = $15

This means that after 3 years you will get $15 as interest. So, the total amount you will have after 3 years will be:

Total amount = Principal + Simple interest = $100 + $15 = $115

What is compound interest?

Compound interest can be a little more exciting than simple interest. Unlike simple interest, compound interest is calculated on both the initial principal and the interest that accumulates over time. This means you earn interest on the interest!

Compound interest formula

Compound interest = Principal × (1 + interest rate) ^ time - Principal

In this formula:

• Principal (P): The initial amount of money.
• Interest Rate (R): The interest rate per time period, usually per year.
• Time (T): The number of time periods for which money is invested or borrowed.
• The symbol "^" means that you raise the number to the power of "times".

Example of compound interest

Imagine you put the same $100 into an account that pays 5% compound interest per year for 3 years. Let's calculate the compound interest:

Principal (P) = $100
Rate of interest (R) = 5% per annum = 0.05
Time (T) = 3 years

Compound interest = 100 × (1 + 0.05)^3 – 100

Compound interest = 100 × (1.157625) - 100 = $15.76

After 3 years you will earn $15.76 in interest. The total amount you will have after 3 years is:

Total amount = Principal + Compound interest = $100 + $15.76 = $115.76

Comparison: simple vs. compound interest

While both simple and compound interest will help you grow your money if you're saving (or cost you more if you're borrowing), compound interest makes your money or loan grow faster because you earn (or pay) interest on the interest.

Visualization example

Text example

Imagine you deposit $200 in two different banks. One bank offers simple interest, and the other bank offers compound interest. Both banks offer 4% interest per year.

Bank A: Simple interest

Principal (P) = $200
Rate of interest (R) = 4% per annum = 0.04
Time (T) = 5 years

Simple interest = 200 × 0.04 × 5 = $40

In Bank A, your total after 5 years:

Total = Principal + Simple Interest = $200 + $40 = $240

Bank B: Compound interest

Principal (P) = $200
Rate of interest (R) = 4% per annum = 0.04
Time (T) = 5 years

Compound interest = 200 × (1 + 0.04)^5 – 200

Compound interest = 200 × (1.2166529) - 200 = $43.33

In Bank B, your total after 5 years:

Total = Principal + Compound Interest = $200 + $43.33 = $243.33

Why is compound interest so powerful?

Compound interest is often called the "eighth wonder of the world" because the longer you keep your money invested, the faster it grows. This means that its growth accelerates over time. Let's see why:

If you invest the interest you earn back into your account, you start earning more interest than your initial amount, on top of the interest you've already earned. The longer you keep your money invested, the bigger it will grow.

This is why many people try to start saving and investing as early as possible. Even a small amount can turn into a large sum in the long run with compound interest.

Conclusion

To summarize, both simple and compound interest methods help your money grow over time. Simple interest is calculated only on the principal amount, making it easier to understand and calculate. On the other hand, compound interest is calculated on both the principal amount and the interest earned, which can help your money grow faster.

Understanding these concepts can be very important when you're thinking about where to invest your money or where to borrow from. Remember, starting saving and investing early takes full advantage of the power of compound interest.

We hope this basic introduction will help you understand interest better. Use these simple examples and visual aids to remember how interest works!

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