A small business owner deposits some money in a fixed-return plan that pays simple interest at a constant annual rate. The deposit grows to Rs. 13,440 after 4 years and to Rs. 16,320 after 7 years. If the same deposit had instead been placed for 2 years in a recurring plan that compounds every 6 months at the same annual rate, then the total interest earned (approximately) would be:

The simple interest earned over the 3 years between year 4 and year 7 is Rs. 16,320 minus Rs. 13,440, which equals Rs. 2,880, making the annual simple interest Rs. 960. The principal is found by subtracting 4 years of interest from the year 4 amount, giving 13440 minus (4 times 960), which equals Rs. 9,600, and the annual interest rate is (960 divided by 9600) times 100, resulting in 10 percent. For a recurring plan compounding every 6 months at this 10 percent annual rate, the biannual rate is 5 percent over 4 periods. The compound amount is 9600 times 1.05 raised to the fourth power, which is approximately Rs. 11,670, making the total compound interest 11670 minus 9600 equal approximately Rs. 2,070.

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