Rachit invests ₹12,000 for a 2-year period at a certain rate of simple interest per annum. Prasad invests ₹12,000 for a 2-year period at the same rate of interest per annum as Rachit, but in Prasad's case the interest is compounded annually. Find the rate of interest per annum if Prasad receives ₹172.80 more as interest than Rachit at the end of the 2-year period.

12%

The formula used here is,

Difference in the simple interest and compound interest on a certain sum at R% per annum in 2 years = (CI - SI) = $\frac{PR^2}{100^2}$

⇒ Difference in the simple interest and compound interest on a 12000 at R% per annum in 2 years = 172.8

⇒ 172.8 = $\frac{12000 × R^2}{100^2}$

⇒  172.8  = 12 x \(\frac{R²}{10}\)

⇒   R²   = 144

⇒   R   = 12%