Grade 8 Compound Interest

Simple Interest: Interest is calculated only on the original principal amount. The interest earned each period is fixed.

Compound Interest: Interest is calculated on the original principal amount **plus** the accumulated interest from previous periods. Interest earns interest, leading to faster growth.

Key Difference: Simple interest grows linearly, while compound interest grows exponentially.

Step 1: The formula to calculate the **Amount (A)** when interest is compounded annually is:
A = P (1 + R/100)ⁿ

Step 2: Explain the terms in the formula:

• **A** = Amount (the total money after interest)
• **P** = Principal (the initial amount of money)
• **R** = Rate of interest per annum (per year)
• **n** = Time period (in years)

Step 3: Once you find the Amount (A), you can calculate the **Compound Interest (CI)** using the formula:
CI = A - P

Step 1: Identify the given values:
Principal (P) = Rs. 10,000
Rate (R) = 5% per annum
Time (n) = 2 years

Step 2: Use the compound interest formula for Amount:
A = P (1 + R/100)ⁿ
A = 10000 (1 + 5/100)²

Step 3: Simplify the expression inside the bracket:
1 + 5/100 = 1 + 0.05 = 1.05
A = 10000 (1.05)²

Step 4: Calculate (1.05)²:
(1.05)² = 1.05 * 1.05 = 1.1025
A = 10000 * 1.1025

Step 5: Calculate the Amount (A):
A = 11025
The Amount is Rs. 11,025.

Step 6: Calculate the Compound Interest (CI):
CI = A - P
CI = 11025 - 10000
CI = 1025
The Compound Interest is Rs. 1,025.

Step 1: Calculate simple interest for the first year on the principal.
Interest for Year 1 = (Principal * Rate * Time) / 100
Interest for Year 1 = (5000 * 4 * 1) / 100 = 200
Amount after Year 1 = Principal + Interest for Year 1 = 5000 + 200 = 5200

Step 2: For the second year, the principal is the amount after Year 1 (Rs. 5200). Calculate simple interest on this new principal.
Interest for Year 2 = (5200 * 4 * 1) / 100 = 208
Amount after Year 2 = Amount after Year 1 + Interest for Year 2 = 5200 + 208 = 5408

Step 3: For the third year, the principal is the amount after Year 2 (Rs. 5408). Calculate simple interest on this principal.
Interest for Year 3 = (5408 * 4 * 1) / 100 = 216.32
Amount after Year 3 = Amount after Year 2 + Interest for Year 3 = 5408 + 216.32 = 5624.32

Step 4: The Amount after 3 years is Rs. 5624.32.

Step 5: Calculate the total Compound Interest:
CI = Total Amount - Original Principal
CI = 5624.32 - 5000 = 624.32
The Compound Interest is Rs. 624.32.