Multiple choice

Naresh borrowed Rs. $5,00,000$ at $10$% p.a. compounded half-yearly. the interest he paid was approx $1,65,500$ find for how much time he borrowed this amount ?

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

Principal = 500,000. Rate = 10% p.a. compounded half-yearly = 5% per half-year. Interest = 165,500. Amount = 665,500. A = P(1 + r/100)^n. 665500 = 500000(1.05)^n. 1.331 = (1.05)^n. Since 1.1^3 = 1.331 and 1.05^6 = 1.34, n=6 half-years = 3 years.

AI explanation

With a principal of 500000 and a 10% annual interest rate compounded half-yearly, the rate per period is 5%. The total amount to be repaid is the principal plus the interest, which is 500000 plus 165500, equaling 665500. Using the compound interest formula, 665500 equals 500000 multiplied by 1.05 raised to the power of n, so 1.05 to the power of n equals 1.331. Since 1.05 to the power of 6 equals 1.331, there are 6 half-yearly periods, making the total time 3 years.

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