A man saves ₹ 5,000 every year and invests it at the end of the year at 10% p.a. compound interest. Calculate the total amount of his savings at the end of the third year.

For the first year:

P = ₹ 5,000, R = 10 %, T = 1 year

$\text{Interest} = \dfrac{P \times R \times T}{100}\\[1em] = \dfrac{5,000 \times 10 \times 1}{100}\\[1em] = \dfrac{50,000}{100}\\[1em] = ₹ 500$

Amount at the end of the first year = P + I

= ₹ 5,000 + 500

= ₹ 5,500

For the second year:

P = ₹ 5,500, R = 10 %, T = 1 year

$\text{Interest} = \dfrac{5,500 \times 10 \times 1}{100}\\[1em] = \dfrac{55,000}{100}\\[1em] = ₹ 550$

Amount at the end of the second year = P + I

= ₹ 5,500 + 550

= ₹ 6,050

For the third year:

The newly invested ₹5,000 remains ₹5,000 since it was invested at the end of the year and does not earn any interest.

Total savings at the end of the third year = 6,050 + 5,500 + 5,000 = ₹ 16,550

Hence, the amount at the end of the third year is ₹ 16,550.