Rs.1000 is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will becomes Rs2000 after

A) 15 Yrs

B) 18 Yrs

C) 20 Yrs

D) $16\frac{2}{3}$ Yrs

E) $13\frac{2}{3}$ Yrs


Option D


After $10$ years, $SI$ $= \frac{(1000\times 5\times 10)}{100}$ = Rs.500

Principal for $11^{th}$ Year $=1000+500$ = 1500

$SI$ $=2000-1500$ = Rs.500

$T$ $=\frac{(100\times SI)}{P\times R}$

$=\frac{ 500\times 100}{1500\times 5}$

$=6\frac{2}{3}$ Yrs.

Total time $=10+6\frac{2}{3}$ $=16\frac{2}{3}$ Yrs