Multiple choice

At a certain simple rate of interest, a given sum amounts to Rs. 13,920 in 3 years, and to Rs. 18,960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to

  1. 3,096

  2. 3,221

  3. 3,180

  4. 3,150
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple interest for 3.5 years (6.5 - 3) is 18960 - 13920 = 5040. Annual interest = 5040 / 3.5 = 1440. Principal = 13920 - 3*1440 = 9600. Rate = (1440/9600) * 100 = 15%. Compounded half-yearly for 2 years (4 periods) at 7.5% per period: Amount = 9600 * (1.075)^4 = 12821. Interest = 12821 - 9600 = 3221.

AI explanation

The simple interest for 3.5 years is the difference between the two amounts, which is Rs. 18,960 minus Rs. 13,920 equals Rs. 5,040. Therefore, the simple interest for one year is 5040 divided by 3.5, which is Rs. 1,440, making the principal 13920 minus (3 times 1440) equals Rs. 9,600. The annual simple interest rate is (1440 divided by 9600) times 100, which equals 15 percent. Using the compound interest formula with a principal of 9600, a biannual rate of 7.5 percent, and 4 time periods, the final amount is 9600 times 1.075 raised to the fourth power, which is approximately Rs. 12,821. Subtracting the principal of 9600 from this final amount yields a compound interest of approximately Rs. 3,221.

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