A man borrows ₹ 5000 at 12 percent compound interest payable every six months. He repays ₹ 1800 at the end of every six months. Calculate the third payment he has to make at the end of 18 months to clear the entire the loan.

For 1st half-year

P = ₹ 5000

R = 12%

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

I = $\dfrac{P \times R \times T}{100} = \dfrac{5000 \times 12 \times \dfrac{1}{2}}{100}$ = ₹ 300.

Amount = P + I = ₹ 5000 + ₹ 300= ₹ 5300.

Money paid at the end of 1st half year = ₹ 1800

Balance money for 2nd half-year = ₹ 5300- ₹ 1800 = ₹ 3500.

For 2nd half-year

P = ₹ 3500

R = 12%

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

I = $\dfrac{P \times R \times T}{100} = \dfrac{3500 \times 12 \times \dfrac{1}{2}}{100}$ = ₹ 210.

Amount = ₹ 3500 + ₹ 210 = ₹ 3710

Money paid at the end of 2nd half-year = ₹ 1800

Balance money for 3rd half-year = ₹ 3710 - ₹ 1800 = ₹ 1910

For 3rd half-year

P = ₹ 1910

R = 12%

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

Interest = $\dfrac{P \times R \times T}{100} = \dfrac{1910 \times 12 \times \dfrac{1}{2}}{100}$ = ₹ 114.60

Amount = ₹ 1910 + ₹ 114.60 = ₹ 2024.60

Hence, amount to be paid at the end of 18 months = ₹ 2024.60