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Simple Interest Split Across Periods

MAT 2018 · Mathematical Skills · Easy · Simple Interest

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The rate of simple interest on a sum of money is 6%6\% per annum for the first 33 years, 8%8\% per annum for the next 55 years and 10%10\% per annum for the period beyond 88 years. If the simple interest accrued by the sum for a total period of 1010 years is Rs. 1,5601,560, what is the sum?

  1. A.

    Rs. 1,500

  2. B.

    Rs. 3,000

  3. C.

    Rs. 2,000

  4. D.

    Data inadequate

Answer

C

Explanation

Total interest percentage over 1010 years:

  • First 33 years at 6%=18%6\% = 18\%
  • Next 55 years at 8%=40%8\% = 40\%
  • Remaining 22 years at 10%=20%10\% = 20\%

Total effective interest rate =18%+40%+20%=78%= 18\% + 40\% + 20\% = 78\%. Given SI =1560= 1560: 0.78P=1560  ⟹  P=15600.78=20000.78 P = 1560 \implies P = \frac{1560}{0.78} = 2000

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