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Compound Interest Principal Calculation

XAT 2015 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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In the beginning of the year 2004, a person invests some amount in a bank. In the beginning of 2007, the accumulated interest is Rs. 10,000 and in the beginning of 2010, the accumulated interest becomes Rs. 25,000. The interest rate is compounded annually and the annual interest rate is fixed. The principal amount is:

  1. A.

    Rs. 16,000

  2. B.

    Rs. 18,000

  3. C.

    Rs. 20,000

  4. D.

    Rs. 25,000

  5. E.

    None of the above

Answer

C

Explanation

Let principal be PP and x=(1+r)3x = (1+r)^3. Interest after 3 years (2007) = P(x−1)=10000P(x - 1) = 10000. Interest after 6 years (2010) = P(x2−1)=25000P(x^2 - 1) = 25000.

Dividing the two equations: P(x2−1)P(x−1)=2500010000  ⟹  x+1=2.5  ⟹  x=1.5\frac{P(x^2 - 1)}{P(x - 1)} = \frac{25000}{10000} \implies x + 1 = 2.5 \implies x = 1.5.

Substitute x=1.5x = 1.5 into P(x−1)=10000P(x - 1) = 10000: P(1.5−1)=10000  ⟹  0.5P=10000  ⟹  P=20,000P(1.5 - 1) = 10000 \implies 0.5 P = 10000 \implies P = 20,000.

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