Multiple choice

Nandan borrowed Rs. $1,00,000$ at $20$% p.a. compounded half-yearly. The maximum interest he can pay was approx $30,000$ at any time find for how much time he can borrow this amount ?

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

Principal = 100000, Rate = 20% p.a. = 10% per half-year. Amount A = P(1 + r/100)^n. Interest = A - P = 100000((1.1)^n - 1) <= 30000. (1.1)^n <= 1.3. For n=1, 1.1. For n=2, 1.21. For n=3, 1.331. So n=2 half-years is 1 year, n=3 half-years is 1.5 years.

AI explanation

With a principal of 100000 and a 20% annual interest rate compounded half-yearly, the rate per period is 10%. The total amount to be repaid is the principal plus the maximum interest, which is 100000 plus 30000, equaling 130000. Using the compound interest formula, 130000 equals 100000 multiplied by 1.1 raised to the power of n, so 1.1 to the power of n equals 1.3. Checking the options for half-yearly periods, 1.1 cubed is approximately 1.331, which is very close to 1.3, meaning there are 3 half-yearly periods. This equals 1 and a half years.

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