Mr. Raina deposits ₹ 1,600 in a bank every year in the beginning of the year, at 5% per annum compound interest. Calculate the amount due to him at the end of 2 years. Also find his gain in two years.

For 1st year,

P = ₹ 1,600

R = 5%

T = 1 year

Using formula,

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

Substituting the values, we get

$\Rightarrow I = \dfrac{1,600 \times 5 \times 1}{100}\\[1em] = 16 \times 5 \\[1em] = 80.$

A = P + I = ₹ 1,600 + ₹ 80 = ₹ 1,680

For 2nd year,

P = ₹ 1,680 + ₹ 1,600 (Amount deposited at beginning of every year) = ₹3,280

R = 5%

T = 1 year

$\Rightarrow I = \dfrac{3,280 \times 5 \times 1}{100}\\[1em] = \dfrac{16,400}{100} \\[1em] = 164.$

A = P + I = ₹ 3,280 + ₹ 164 = ₹ 3,444.

Gain = Total balance - money invested

= ₹ 3,444 - (₹ 1,600 x 2)

= ₹ 3,444 - ₹ 3,200

= ₹ 244.

Hence, at the end of 2 years amount = ₹ 3,444 and the gain = ₹ 244.