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Rocky lent a sum of Rs.100 at simple interest of 6% p.a. for the first month, 12% p.a. for the second month, 24% p.a. for the third month, and so on. Find the total amount of interest earned at the end of one year.
1. Rs. 2145
2. Rs. 2130.5
3. Rs. 2055
4. Rs. 2095.6
5. Rs. 2047.5

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Best answer
Correct Answer - Option 5 : Rs. 2047.5

Calculation:

Principal = Rs. 100

Rate of Interest for 1st month = 6%

Interest = 6/12

Interest for second month = 12/12

The interest earned for the successive months is in the form of geometric progression.

Rs. 6/12, Rs. 12/12, Rs. 24/12 ……

a = Rs. 6/12, r = (12/12)/ (6/12) = 2, where a is the first term and r is the common ratio of the series

∴ Sum of series = a(rn - 1)/r – 1

⇒ 6/12(212 - 1)/2 – 1

⇒ ½(4096 – 1)

⇒ Rs. 2047.5

The total amount of interest earned at the end of one year is Rs. 2047.5.

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