The ratio of difference between simple interest and compound interest of a certain sum of money for 2 years and for 3 years is 5: 16. Then rate of interest is एक निश्चित धनराशि पर 2 वर्ष तथा 3 वर्ष के साधारण ब्याज और चक्रवृद्धि ब्याज के अन्तर में अनुपात 5: 16 है | ब्याज की दर है

For amount P at rate r%, CI for n years = P[(1+r/100)ⁿ - 1], SI = P × n × r/100. Difference for 2 years: P[(1+r/100)² - 1 - 2r/100] = P(r²/10000). Difference for 3 years: P[(1+r/100)³ - 1 - 3r/100]. Given ratio of differences = 5:16. After simplification, we get r²/10000 : (r²/10000)(3+r/100) = 5:16. So (3+r/100) = 16/5, giving r/100 = 1/5, r = 20%.