If simple interest for 2 years for a sum is Rs.600 and compound interest for the same sum for 2 years at same rate of interest is Rs.645, what will be the rate of interest?

15%

Simple interest for 1st year = \(\frac{ 600}{2 }\) = 300

Simple interest for 2nd year = 600 - 300 = 300

Compound interest for 1st year is always same as the simple interest of 1st year so it comes out to be 300

Compound interest for the 2nd year = 645 - 300 = 345

Thus, rate of interest = \(\frac{45 }{ 300}\) x 100 = 15% (345 - 300 = 45)