Option 1 : Rs. 400

Given:

P = 10000

R = 20%

T = 2 years

**Formula used:**

**\(A\; = \;P{\left[ {1 + \frac{R}{{100}}} \right]^T}\)**

CI = A – P

\(SI = \frac{{P \times {\rm{R}} \times {\rm{T}}}}{{100}}\)

Where,

A = Amount

CI = Compound interest

SI = Simple interest

P = Principal amount

R = Rate of interest

T = Time period

**Calculations:**

Joe’s interest = SI = (10000 × 20 × 2)/100

⇒ 1000 × 4

⇒ Rs.4000

Ben’s interest = CI = 10000 × [1 + (20/100)]^{2} – 10000

⇒ 10000 × [(6/5)^{2} – 1]

⇒ 10000 × (36 - 25)/25

⇒ 400 × 11

⇒ Rs.4400

⇒ Difference in interests = Rs. 4400 – Rs. 4000 = Rs. 400

**∴ The difference between the interests earned by Ben and Joe is Rs.400**

__Alternate Method__

Convert percentage into fraction

20% = 1/5

⇒ SI = 2000 + 2000 = 4000

⇒ CI = 2000 + 2000 + 400 = 4400

⇒ CI – SI = 400

**∴ Difference between the interests is Rs.400**

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