Question

If Rs 1000 be invested at interest rate of 5% and the interest be added to the principal every 10 years, then the number of years in which it will amount to Rs 2000 is:

• A. $16\frac{2}{3}years$
  
• B. $16\frac{1}{4}years$
  
• C. 16 years
  
• D. 15 years
• E. None of these

Answer 1

The correct option is A $16\frac{2}{3}years$


The interest earned in 10 years on Rs 1000 at 5% per annum
$\frac{1000\times 5\times 10}{100}=Rs500.$
The principal now becomes =Rs 1000+Rs 500 =Rs 1500.
We now find the time in which Rs 1500 become Rs 2000 at $5\%$ p.a.
P =Rs 1500, A =Rs 2000,
I =A -P =200-1500 =Rs 500, R =5% p.a.
$\therefore$ Time (T)$=\frac{100\times I}{R\times P}=\frac{100\times 500}{5\times 1500}=6\frac{2}{3}years.$
$\therefore$ Total time $=(10+6\frac{2}{3})years=16\frac{2}{3}years.$