Multiple choice

Find the compound interest for Rs. $1,000$ for $4$ years at $5\%$ p.a. When it is compounded half-yearly.

  1. $220$
  2. $218$
  3. $215$
  4. $250$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Principal = 1000, Rate = 5% p.a. compounded half-yearly (2.5% per half-year), Time = 4 years (8 periods). Amount = 1000 * (1.025)^8 = 1000 * 1.2184 = 1218.4. Interest = 1218.4 - 1000 = 218.4, which rounds to 218.

AI explanation

When compounded half-yearly for 4 years, the number of conversion periods is 4 x 2 = 8, and the half-yearly rate is 5% / 2 = 2.5%. Using the compound amount formula, A = 1000 x (1 + 2.5/100)^8 = 1000 x (1.025)^8 = 1218.40. Subtracting the principal of Rs. 1000 gives a compound interest of Rs. 218.40, which rounds to Rs. 218.

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