Compound interest

Key notes:

💡 What is Compound Interest?

  • Compound Interest (CI) is the interest calculated on the principal + previously earned interest.
  • It is called “interest on interest.”

🧮 Important Terms

  • Principal (P): The original amount of money
  • Rate of Interest (R): Percentage charged per year
  • Time (T): Number of years
  • Amount (A): Total money after interest is added

📐 Formula for Compound Interest

  • Amount:

A = P (1 + R/100)T

  • Compound Interest:

CI = A − P

⏰ Compounding Periods

  • Annually: Interest added once a year
  • Half-yearly: Interest added twice a year
  • Quarterly: Interest added four times a year

📌 For half-yearly:

A = P (1 + R/200)2T

📈 Simple Interest vs Compound Interest

  • Simple Interest: Calculated only on principal
  • Compound Interest: Calculated on principal and previous interest
  • CI is always greater than SI for the same P, R, and T (except for 1 year)

📝 Example

  • P = ₹1000, R = 10% per year, T = 2 years

A = 1000 (1 + 10/100)2 = 1000(1.1)2 = ₹1210

CI = 1210 − 1000 = ₹210

🏦 Where Compound Interest is Used

  • Bank savings accounts
  • Fixed deposits
  • Investments
  • Loans and credit cards

⭐ Key Takeaways

  • Compound interest helps money grow faster over time
  • More frequent compounding = more interest
  • Useful for saving and investing wisely

Learn with an example

To the nearest paisa, how much interest will she earn in 3 years?

Greta has ₹30 in a savings account that earns 5% interest, compounded annually.

Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.₹——–

Write the rate as a decimal.

5%=0.05

Calculate the balance.

B = p(1 + r)t

=₹30(1+0.05)3

=₹30(1.05)3

=₹30(1.157625)

=₹34.72875

Now use this to find the interest, which is the balance minus the principal.

₹34.72875 − ₹30 = ₹4.72875

Round to the nearest paisa.

₹4.72875 →  ₹4.73

To the nearest paisa, the interest will be ₹4.73.

To the nearest paisa, how much interest will she earn in 3 years?

Krysta deposited ₹40 in a savings account earning 5% interest, compounded annually.

Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.₹——–.

Write the rate as a decimal.

5%=0.05

Calculate the balance.

B = p(1 + r)t

=₹40(1+0.05)3

=₹40(1.05)3

=₹40(1.157625)

=₹46.305

Now use this to find the interest, which is the balance minus the principal.

₹46.305 − ₹40 = ₹6.305

Round to the nearest paisa.

₹6.305 →  ₹6.31

To the nearest paisa, the interest will be ₹6.31.

To the nearest paisa, how much interest will she earn in 2 years?

Madelyn has ₹90 in a savings account. The interest rate is 5%, compounded annually.

Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.₹——–.

Write the rate as a decimal.

5%=0.05

Calculate the balance.

B = p(1 + r)t

=₹90(1+0.05)3

=₹90(1.05)3

=₹90(1.157625)

=₹99.225

Now use this to find the interest, which is the balance minus the principal.

₹99.225 − ₹90 = ₹9.225

Round to the nearest paisa.

₹9.225 →  ₹9.23

To the nearest paisa, the interest will be ₹9.23.

let’s practice!