The total compound interest accrued on a sum after 2 years, invested at a certain rate of interest compounded annually, is 8⅓% more than the total simple interest accrued on the same sum invested at the same rate of interest after the same time period. The total compound interest accrued on the same sum after 3 years will be what percent (to the nearest integer) more than the total simple interest accrued on it?

CI - SI for 2 years = P * r^2 / 100^2. SI for 2 years = P * 2r / 100. Given (P * r^2 / 10000) / (P * 2r / 100) = 1/12 (since 8 1/3% = 1/12). r/200 = 1/12, so r = 200/12 = 50/3 = 16.67%. For 3 years, CI = P(1 + r/100)^3 - P, SI = P * 3r / 100. CI/SI = ((1+r/100)^3 - 1) / (3r/100). With r=50/3, (1+1/6)^3 - 1 = (7/6)^3 - 1 = 343/216 - 1 = 127/216. SI = 3 * (50/3) / 100 = 0.5. Ratio = (127/216) / 0.5 = 127/108 = 1.1759. Percent more = 17.59%, nearest to 18%.