At the beginning of year 2011, a man had ₹ 22,000 in his bank account. He saved some money by the end of this year and deposited it in the bank. The bank pays 10% per annum compound interest and at the end of year 2012 he had ₹ 39,820 in his bank account. Find, what amount of money he had saved and deposited in his account at the end of year 2011 .

Given:

Initial amount at the beginning of 2011 = ₹ 22,000

Rate of interest = 10 %

Total amount at the end of 2012 = ₹ 39,820

Let ₹ x be the amount the man saved and deposited at the end of 2011.

For compound interest:

P = ₹ 22,000, R = 10 %, T = 1 years

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

= 22,000 $\Big(1 + \dfrac{10}{100}\Big)^1$

= 22,000 x (1 + 0.1)

= 22,000 x (1.1)

= 24,200

Thus, before depositing the additional savings, the account balance was ₹ 24,200 at the end of 2011.

For compound interest:

P = ₹ (24,200 + x), R = 10 %, T = 1 years, A = ₹ 39,820

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

⇒ 39,820 = (24,200 + x) $\Big(1 + \dfrac{10}{100}\Big)^1$

⇒ 39,820 = (24,200 + x) $\times$ (1 + 0.1)

⇒ 39,820 = (24,200 + x) $\times$ (1.1)

⇒ (24,200 + x) = $\dfrac{39,820}{1.1}$

⇒ (24,200 + x) = 36,200

⇒ x = 36,200 - 24,200 = 12,000

Hence, ₹ 12,000 was saved and deposited in his account at the end of year 2011.