The difference between compound interest and simple interest on a sum for 2 year at 20% per annum is Rs. 200. If the interest is compounded… — Answer & Discussion

The difference between compound interest and simple interest on a sum for 2 year at 20% per annum is Rs. 200. If the interest is compounded half yearly, then what is the difference (in Rs) between compound and simple interest for 1st year?

A50
B75
C100
D150

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Discussion 1

CCommunity16 Jul 2019

Given,

⇒ CI – SI = Rs. 200

Let the principal be P

So, we have

⇒ P(1 + R/100n)nt – P - (P × R × T)/100 = 200

⇒ P(1 + 20/100)2 – P - (P × 20 × 2)/100 = 200

⇒ 1.44P – P – 0.4P = 200

⇒ 0.04P = 200

⇒ P = 200/0.04 = Rs. 5000

Now, the difference when compounded half yearly

⇒ [5000(1 + 20/200)2 – 5000] – (5000 × 20 × 1)/100

⇒ [5000(1.1)2 – 5000] – 1000

⇒ [5000(1.21) – 5000] – 1000

⇒ 6050 – 6000 = Rs. 50

∴ the correct option is 1)