Multiple choice

An amount of money was invested under compound interest for three years at a certain rate of interest compounded annually. It was found that the sum of the interests accrued for the first and the second year was ₹1560 and the total amount after three years was seven times the interest accrued for the third year. Which of the following gives the value, in ₹, of the amount of money invested?

  1. 2160

  2. 3600

  3. 4320

  4. 3240
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be principal and r be rate. Interest 1st year = Pr. Interest 2nd year = Pr(1+r). Sum = Pr(2+r) = 1560. Amount after 3 years = P(1+r)^3. Interest 3rd year = P(1+r)^3 - P(1+r)^2 = P(1+r)^2 * r. Given P(1+r)^3 = 7 * P(1+r)^2 * r => 1+r = 7r => 6r = 1 => r = 1/6. Pr(2+1/6) = 1560 => Pr(13/6) = 1560 => Pr = 720. P(1/6) = 720 => P = 4320.

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