Compound Interest

Compound Interest is a way to calculate how much money you will have (or owe) after interest is added to your principal (the original amount of money). What makes compound interest different from simple interest is that each time interest is added, it's added to the new total amount. This means you earn (or owe) interest on the interest from previous periods, which can make the amount grow faster.

Key Terms You Need to Know:

Principal: The amount of money you start with (either invested or borrowed).
Interest: The extra money that is added by the bank (or owed to the bank) based on the principal.
Rate: The percentage at which the interest is added. This is usually given per year.
Amount or Final Value: The total amount of money you have (or owe) at the end of the time period after all the interest has been added.

How to Calculate Compound Interest Using the Formula

To calculate compound interest quickly and easily, you can use a formula. This formula works when the interest rate stays the same each year and no extra money is added or taken out during the time period.

The formula is: $F = P(1 + i)^t$

$F$ is the final amount (the total you'll have at the end).
$P$ is the principal (the starting amount).
$i$ is the rate of interest as a decimal (e.g., 5% becomes 0.05).
$t$ is the time in years that the money is invested or borrowed for.

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Exam Tip:

Remember, this formula is in your Formulae and Tables book, so you don't need to memorise it. Make sure you know where to find it so you can use it during your exam!

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Step-by-Step Example Using the Formula

Let's work through an example to see how this formula is used. Imagine you invest €1,000 at an interest rate of 5% per year for 3 years.

Step 1: Convert the Interest Rate to a Decimal

Interest rates are usually given as percentages, but for the formula, we need to convert the percentage to a decimal.
5% becomes 0.05 (just divide by 100).

Step 2: Substitute the Values into the Formula

Plug the values into the formula: $F = 1,000(1 + 0.05)^3$

Step 3: Add $1$ to the Interest Rate

Inside the brackets, add $1$ to the interest rate (as a decimal): $1 + 0.05 = 1.05$

Step 4: Raise This Number to the Power of the Number of Years

Now, raise 1.05 to the power of 3 (because the money is invested for 3 years): $1.05^3 = 1.157625$

Step 5: Multiply by the Principal

Finally, multiply the result by the principal (€1,000): $F = 1,000 \times 1.157625 = €1,157.63$ Final Answer:
After 3 years, the final amount of money you will have is €1,157.63.

Explanation of Each Step:

Why convert the interest rate to a decimal? The formula requires the interest rate in decimal form to correctly calculate how much interest is added.
Why add $1$ to the interest rate? Adding 1 ensures that when you multiply, you are calculating both the original amount (principal) and the interest together.
Why raise it to the power of the number of years? Raising the number to the power of the number of years calculates how the interest compounds (grows) over multiple years.
Why multiply by the principal? This step calculates the final total amount by applying the compounded interest to the original amount.

Compound Interest Simplified Revision Notes for Junior Cycle Mathematics