Calculate Simple Interest for A

Person A deposited ₹8,000 at 8% simple interest for 3 years. The formula for simple interest (SI) is:

$ SI = \frac{P \times R \times T}{100} $

Where:

• $ P $ = Principal amount = ₹8,000
• $ R $ = Rate of interest per annum = 8%
• $ T $ = Time period = 3 years

Substituting the values:

$ SI_A = \frac{8000 \times 8 \times 3}{100} $

$ SI_A = 80 \times 8 \times 3 $

$ SI_A = 640 \times 3 $

$ SI_A = ₹1,920 $

Calculate Compound Interest for B

Person B deposited ₹6,000 at 10% compound interest per annum for 3 years. The formula for the amount (A) after compound interest is:

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

Where:

• $ P $ = Principal amount = ₹6,000
• $ R $ = Rate of interest per annum = 10%
• $ T $ = Time period = 3 years

First, calculate the total amount (A) after 3 years:

$ A_B = 6000 \left(1 + \frac{10}{100}\right)^3 $

$ A_B = 6000 \left(1 + 0.1\right)^3 $

$ A_B = 6000 \left(1.1\right)^3 $

$ A_B = 6000 \times 1.331 $

$ A_B = ₹7,986 $

The compound interest (CI) earned is the total amount minus the principal:

$ CI_B = A_B - P $

$ CI_B = 7986 - 6000 $

$ CI_B = ₹1,986 $

Determine Interest Difference

The difference between their interests is the absolute difference between the compound interest earned by B and the simple interest earned by A.

Difference = $ CI_B - SI_A $

Difference = $ ₹1,986 - ₹1,920 $

Difference = $ ₹66 $

The difference between their interests after 3 years is ₹66.