Rachna borrows ₹ 12000 at 10 per cent per annum interest compounded half-yearly. She repays ₹ 4000 at the end of every six months. Calculate the third payment she has to make at the end of 18 months in order to clear the entire loan.

For 1st half-year

P = ₹ 12000

R = 10%

T = $\dfrac{1}{2}$ year

I = $\dfrac{P \times R \times T}{100} = \dfrac{12000 \times 10 \times \dfrac{1}{2}}{100}$ = ₹ 600.

Amount = P + I = ₹ 12000 + ₹ 600= ₹ 12600.

Money paid at the end of 1st half year = ₹ 4000

Balance money for 2nd half-year = ₹12600- ₹4000 = ₹8600.

For 2nd half-year

P = ₹ 8600

R = 10%

T = $\dfrac{1}{2}$ year

I = $\dfrac{P \times R \times T}{100} = \dfrac{8600 \times 10 \times \dfrac{1}{2}}{100}$ = ₹ 430.

Amount = ₹ 8600 + ₹ 430= ₹ 9030

Money paid at the end of 2nd half-year = ₹ 4000

Balance money for 3rd half-year = ₹ 9030- ₹ 4000 = ₹ 5030

For 3rd half-year

P = ₹ 5030

R = 10%

T = $\dfrac{1}{2}$ year

Interest = $\dfrac{P \times R \times T}{100} = \dfrac{5030 \times 10 \times \dfrac{1}{2}}{100}$ = ₹ 251.50

Amount = ₹ 5030 + ₹ 251.50 = ₹ 5281.50

Hence, amount to be paid at the end of 18 months = ₹ 5281.50