Compound Interest

What is Compound Interest?

With Compound Interest, you earn interest on both the principal (the original amount) and the interest that’s been added so far. Each year, the interest is calculated on the new amount, not just the starting amount. This means the amount grows faster over time

The Formula for Compound Interest

The compound interest formula looks a bit more complex than the one for simple interest, but it's incredibly powerful:

$$A = P \times \left(1 + \frac{R}{100}\right)^{T}$$

Where:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial sum of money).
• $R$ is the annual interest rate (decimal).
• $T$ is the time the money is invested or borrowed for, in years.

The Power of Compounding

The magic of compound interest really shines over long periods. 

Let’s say you invest $\pounds 200$ at a $5\%$ compound interest rate per year. After the first year, interest is calculated on $\pounds 200$, but in the second year, it’s calculated on the new amount (the original amount + the interest from year one). This continues every year, and your money grows faster because of this “compounding effect.”

 

Example : Finding the Total Amount with Compound Interest

Question: You invest $\pounds 100$ at a compound interest rate of $10\%$ per year for 3 years. What will the total amount be?

1. Identify the values

   • Principal $P = 100$
   • Rate $R = 10$
   • Time $T = 3$
2. Plug into the formula: $$A = 100 \times \left(1 + \frac{10}{100}\right)^{3}$$
3. Calculte: $$A = 100 \times (1 + 0.1)^3 = 100 \times (1.1)^3$$
4. Expand: $$A = 100 \times 1.331 = 133.1$$