Question

Rs. $1500$ is invested at a rate of $10\%$ simple interest and interest is added to the principal after every $5$ years. In how many years will it amount to Rs. $2500$?

• A. $6\frac{1}{9}$ years
• B. $6\frac{1}{4}$ years
• C. $7$ years
• D. $6$ years

Answer 1

The correct option is A $6\frac{1}{9}$ years

Rs.1500 is invested at a rate of $10\%$ simple interest and interest is added to the principal after every $5$ years.

S.I. for the first $5$ years $=1500\times \frac{10}{100}\times 5$

$=$ Rs.$750$

Thus, principal for the next $5$ years is $=$ Rs. $(1500+750)$

$=$ Rs $2250$

Required amount $=$ Rs.$2500$

Let the invested amount amounts to Rs. $2500$ in $t$ years.

So, $2500=2250+2250\times \frac{10}{100}\times t$

$\Rightarrow 2500-2250=225\times t$

$\Rightarrow 225\times t=250$

$\Rightarrow t=\frac{250}{225}$

$\Rightarrow t=\frac{10}{9}$

Thus, total time required $=(5+\frac{10}{9})$ years

$=\frac{45+10}{9}$ years

$=\frac{55}{9}$ years

$=6\frac{1}{9}$ years