Multiple choice

Raman took a loan of some amount and at the end of 2 years, he paid Rs. 54,121.6. The loan was taken at 4% rate of interest, compounded semi-annually. Find the principal amount.

  1. Rs. 40,000

  2. Rs. 46,000

  3. Rs. 50,000

  4. Rs. 42,000

  5. Rs. 44,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The formula for compound interest compounded semi-annually is A = P(1 + r/200)^(2n). Here, A = 54121.6, r = 4, and n = 2, so 54121.6 = P(1 + 2/100)^4 = P(1.02)^4. Calculating (1.02)^4 gives approximately 1.082432, and 54121.6 / 1.082432 = 50000.

AI explanation

Using the compound interest formula A equals P times (1 plus R divided by 100) raised to the power of n, where R is the rate per period and n is the number of periods, we have 54121.6 equals P times (1 plus 0.02) raised to the power of 4. This simplifies to 54121.6 equals P times 1.02 raised to the power of 4, which is P times 1.08243216. Solving for P gives 54121.6 divided by 1.08243216, which equals 50000. The principal amount is Rs. 50,000.

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