Multiple choice

In how many rears will a sum of Rs. $800$ at $10 \%$ per annum compound interest, compounded semiannually becomes Rs. $926.10$?

  1. $1$ year
  2. $3$ years
  3. $2$ years
  4. $\displaystyle 1\frac{1}{2}$years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A = P(1 + r/200)^(2n). 926.10 = 800(1 + 10/200)^(2n) = 800(1.05)^(2n). 926.1/800 = 1.157625. (1.05)^3 = 1.157625. So 2n = 3, n = 1.5 years.

AI explanation

Using the compound interest formula A = P * (1 + R/(2*100))^(2n) for semiannual compounding, we substitute the values to get 926.10 = 800 * (1 + 10/200)^(2n). This simplifies to 926.10 / 800 = (21/20)^(2n), resulting in 1.157625 = (21/20)^(2n). Since 1.157625 is the cube of 1.05, we find that 2n = 3, meaning n equals 1.5 years.

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