Multiple choice

In how much time will Rs. 25,60,000 invested at 5% p.a. fetch an interest of Rs. 2,65,761, the interest being compounded half-yearly?

  1. 4 years

  2. 3 years

  3. 2 years

  4. 1 year

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

Using the compound interest formula A = P(1 + r/n)^(nt), where A = 25,60,000 + 2,65,761 = 28,25,761, P = 25,60,000, r = 0.05, and n = 2 (half-yearly). Solving for t gives (1.025)^(2t) = 2825761/2560000 = 1.1038. Since 1.025^4 is approximately 1.1038, 2t = 4, so t = 2 years.

AI explanation

Adding the principal of Rs. 25,60,000 to the compound interest of Rs. 2,65,761 gives a total amount of Rs. 28,25,761. Using the compound interest formula A = P(1 + R/100)^n with a half-yearly rate of 2.5%, we get 2825761 = 2560000 * (1.025)^n, which simplifies to (1.025)^n = 1.10408. Since 1.025 raised to the 4th power is approximately 1.10408, n equals 4 half-years, making the total time 2 years.

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