32 vote
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?
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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?
1). 50
2). 75
3). 100
4). 150
1 answers
33 vote
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)