Multiple choice

If the difference of simple interest of two years of a sum and compound interest of 1 year and interest is calculated half yearly at a rate of 10% is Rs. 97.5 then find out the sum?

  1. Rs. 1260

  2. Rs. 1000

  3. Rs. 2000

  4. Rs. 1500

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For compound interest calculated half-yearly at 10% annual rate, rate per half-year = 5%. After 1 year (2 half-years), amount = P(1.05)² = P(1.1025), so CI for 1st year = 0.1025P. SI for 2 years at 10% = 0.20P. Difference = SI(2 years) - CI(1 year) = 0.20P - 0.1025P = 0.0975P = 97.5. Solving: P = 97.5/0.0975 = 1000. Option A (1260) incorrectly uses different compounding assumptions.

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