A man borrows ₹ 5,000 at 12% compound interest p.a., interest payable every six months. He pays back ₹ 1,800 at the end of every six months. The third payment he has to make at the end of 18 months in order to clear the entire loan will be:

1. ₹ 2,024.60

2. ₹ 2,204.60

3. ₹ 2,240.60

4. ₹ 2,402.60

For first six moths :

P = ₹ 5,000

T = 6 months = 0.5 year

R = 12%

I = $\dfrac{P \times R \times T}{100}$

$= \dfrac{5000 \times 12 \times 0.5}{100}$ = ₹ 300.

Amount = P + I = ₹ 5,000 + ₹ 300 = ₹ 5,300.

Amount payed at end of six months = ₹ 1,800.

Amount left at beginning of second six months = ₹ 5,300 - ₹ 1,800 = ₹ 3,500.

For next six months :

P = ₹ 3,500

R = 12%

T = 6 months = 0.5 year

I = $\dfrac{P \times R \times T}{100}$

$= \dfrac{3500 \times 12 \times 0.5}{100}$ = ₹ 210.

Amount = P + I = ₹ 3,500 + ₹ 210 = ₹ 3,710.

Amount payed at end of second six months = ₹ 1,800.

Amount left at beginning of third six months = ₹ 3,710 - ₹ 1,800 = ₹ 1,910

For next six months :

P = ₹ 1,910

R = 12%

T = 6 months = 0.5 year

I = $\dfrac{P \times R \times T}{100}$

$= \dfrac{1910 \times 12 \times 0.5}{100}$ = ₹ 114.6

Amount due at the end of third year = P + I = ₹ 1,910 + ₹ 114.6 = ₹ 2,024.60

Hence, option 1 is correct option.