A sum of ₹ 16,000, invested at simple interest, amounts to ₹ 22,400 in 4 years at a certain rate of interest. If the same sum of money is invested for 2 years at the same rate of interest, compounded p.a., find the compound interest earned.

Given: Principal = ₹ 16,000

Amount after 4 years at S.I. = ₹ 22,400

Time = 4 years

Let r% be the rate of interest.

A = P + SI

⇒ 22,400 = 16,000 + SI

⇒ SI = 22,400 - 16,000 = ₹ 6,400

Using the formula,

I = $\dfrac{P \times R \times T}{100}$

⇒ 6,400 = $\dfrac{16,000 \times r \times 4}{100}$

⇒ 6,400 = 640r

⇒ r = $\dfrac{6,400}{640}$ = 10%

For compound interest:

P = ₹ 16,000, R = 10 %, T = 2 years

A = P $\Big(1 + \dfrac{R}{100}\Big)^n$

= 16,000 $\Big(1 + \dfrac{10}{100}\Big)^2$

= 16,000 $(1 + 0.1)^2$

= 16,000 $(1.1)^2$

= 16,000 x 1.21

= 19,360

CI = A - P

= 19,360 - 16,000 = ₹ 3,360

Hence, the compound interest earned = ₹ 3,360.