Multiple choice

Ankit deposited a certain amount in a bank for 2 years at 20% compound interest per annum. The same amount would have given Rs. 1928 more in interest, if it were put in a scheme providing 20% per annum interest compounded on a half-yearly basis. What was the sum that Ankit deposited in the bank?

  1. Rs. 20,000

  2. Rs. 40,000

  3. Rs. 60,000

  4. Rs. 80,000

  5. Rs. 10,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the sum be P. Annual interest = P * ((1 + 0.2)^2 - 1) = 0.44P. Half-yearly interest = P * ((1 + 0.1)^4 - 1) = P * (1.4641 - 1) = 0.4641P. The difference is 0.4641P - 0.44P = 0.0241P = 1928. P = 1928 / 0.0241 = 80000.

AI explanation

The effective annual rate for half-yearly compounding at 20% is calculated as (1 + 0.10) raised to the power of 2 minus 1, resulting in 21% per annum. The difference in interest for 2 years on a principal P between a 21% annual rate and a 20% annual rate is derived from the respective compound amounts: P multiplied by (1.21 squared minus 1) minus P multiplied by (1.20 squared minus 1), which simplifies to P multiplied by 0.0241. Setting this difference equal to Rs. 1928 gives P equals 1928 divided by 0.0241, which equals Rs. 80,000, meaning the sum deposited was Rs. 80,000.

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