Answer : Option C

Explanation :

$MF#%\text{Amount after 3 years on Rs.20000 at 10% compound interest }\\\\=20000\left(1 + \dfrac{10}{100}\right)^3
= 20000\left(\dfrac{11}{10}\right)^3 = 26620 \quad \color{#F00}{\text{--- (1)}}$MF#%
He paid Rs.2000 after 1st year.
Hence Rs.2000 and its compound interest for 2 years (i.e., amount on 2000 after 2 year) need to be reduced from (1)
Similarly, he paid Rs.2000 after 2nd year.
Hence Rs.2000 and and its compound interest for 1 year (i.e., amount on 2000 after 1 year) need to be reduced from (1)
Similarly, he paid Rs.2000 after 3rd year.
Hence this Rs.2000 also need to be reduced from (1)
Hence, remaining amount
$MF#%= 26620 - 2000\left(1 + \dfrac{10}{100}\right)^2 - 2000\left(1 + \dfrac{10}{100}\right)^1 - 2000\\\\ = 26620 - 2000\left(\dfrac{11}{10}\right)^2 - 2000\left(\dfrac{11}{10}\right) - 2000\\\\ = 26620 - 2420 - 2200 - 2000 \\\\ = 20000$MF#%
i.e, he still owes Rs.20000 even after three installments