Ratnesh lent a sum of Rs.100 at simple interest of 6% p.a. for the first month, 12% p.a. for the second month, 24% p.a. for the third month and so on. What is the total amount of interest earned at the end of one year?

Monthly rates form GP: 6%, 12%, 24%, 48%, ... doubling each month. For 12 months at simple interest on Rs.100: Total interest = sum of (100 × rate × 1/12 × 1/100) = (1/12) × sum of rates in %. Sum = 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072 + 6144 + 12288 = 24570. Interest = 24570/12 = 2047.5. The GP sum is a(r^n-1)/(r-1) = 6(2^12-1)/(2-1) = 6(4095) = 24570 paise = Rs. 2047.5.