A man borrows ₹ 10000 at 5% per annum compound interest. He repays 35% of the sum borrowed at the end of the first year and 42% of the sum borrowed at the end of the second year. How much must he pay at the end of the third year in order to clear the debt ?

For first year :

P = ₹ 10000

R = 5%

T = 1 year

I = $\dfrac{P \times R \times T}{100} = \dfrac{10000 \times 5 \times 1}{100}$ = ₹ 500

Amount = P + I = ₹ 10000 + ₹ 500 = ₹ 10500

35% of the sum borrowed is repaid at the end of the first year.

Sum repaid = $\dfrac{35}{100} \times 10000$ = ₹ 3500

Sum left = Amount - Sum repaid = ₹ 10500 - ₹ 3500 = ₹ 7000

For second year :

P = ₹ 7000

R = 5%

T = 1 year

I = $\dfrac{P \times R \times T}{100} = \dfrac{7000 \times 5 \times 1}{100}$ = ₹ 350

Amount = P + I = ₹ 7000 + ₹ 350 = ₹ 7350

42% of the sum borrowed is repaid at the end of the second year.

Sum repaid = $\dfrac{42}{100} \times 10000$ = ₹ 4200

Sum left = Amount - Sum repaid = ₹ 7350 - ₹ 4200 = ₹ 3150

For third year :

P = ₹ 3150

R = 5%

T = 1 year

I = $\dfrac{P \times R \times T}{100} = \dfrac{3150 \times 5 \times 1}{100}$ = ₹ 157.50

Amount = P + I = ₹ 3150 + ₹ 157.50 = ₹ 3307.50

Hence, amount to be paid after the end of third year = ₹ 3307.50