A certain sum of money amounts to ₹8,928 in two years and to ₹10,224 in $3\frac{1}{2}$ years, both at simple interest. The rate of interest per annum is:

12%

Simple Interest = \(\frac{Principal ×Rate × Time }{100}\)

ATQ,

Time span = 2 - 3\(\frac{1}{2 }\) = \(\frac{3 }{2}\) 

Simple interest of \(\frac{3 }{2}\) years = 10224 - 8928 = 1296

Simple interest of 1 years = \(\frac{2 }{3 }\) × 1296 = 864

Simple interest of 2 years = 864 × 2 = 1728

Principal = 8928 - 1728 = 7200

By using formula of simple interest,

1728 = \(\frac{7200 × Rate × 2 }{100}\)

Rate = \(\frac{1728× 100 }{7200×2}\)

= \(\frac{1728 }{72×2}\)

= 12%