Multiple choice

Lakshman and Jay are exploring investment options. Lakshman invests Rs. 18,000 at a 5% rate, compounded annually, and Rs. 16,000 at a 10% rate, compounded semi-annually, both for two years. Meanwhile, Jay decides to invest her money at a 5.8% simple interest rate for six years. Interestingly, both Lakshman and Jay end up receiving the same amount of interest. What is the amount, in rupees, that Jay initially invested?

  1. 13,690

  2. 14,210

  3. 15,210

  4. 15,490

  5. a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Lakshman interest: 18000 * ((1.05)^2 - 1) + 16000 * ((1.05)^4 - 1) = 18000 * 0.1025 + 16000 * 0.215506 = 1845 + 3448.1 = 5293.1. Jay interest: P * 0.058 * 6 = 0.348P. 0.348P = 5293.1. P = 15210.

AI explanation

Lakshman's first investment earns compound interest of 18000 * (1.05)^2 - 18000 = 1845, and his second investment earns 16000 * (1.05)^2 - 16000 = 2640, giving a total interest of 4485. To match this with simple interest over 6 years, Jay must earn 4485 = (Principal * 5.8 * 6) / 100. Solving for Jay's principal gives Principal = 448500 / 34.8 = 15210.

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