Question

Rajesh deposits certain amount in a bank with becomes three times of itself in 16 years find the time required by the same amount to become 4 times itself at the same rate of interest the interest is not compounded

Answer 1

Answer:

24 years.

Step-by-step explanation:

Let the initial amount = x,

Suppose r be the annual rate of interest,

Thus, the total amount after 16 years,

$A=x+\frac{16rx}{100}$

According to the question,

A = 3x

$\implies x+\frac{16rx}{100}=3x$

$\frac{4rx}{25}=2x$

$\frac{4r}{25}=2$

$\implies r = \frac{25}{2}\%$

Thus, the annual rate of interest = 25/2 %,

Let after t years the amount will be 4 times to itself.

$\implies x + \frac{x\times \frac{25}{2}\times t}{100}=4x$

$1+\frac{25t}{200}=4$

$\frac{t}{8}=3$

$\implies t = 24\text{ years}$

Answer 2

Answer:

Let the sum of money (principal) be Rs. 100

∴ A.T.Q. -

Amount=3×principal

∴ Amount = 3×100

=Rs. 300

∵Interest(I) = (A)Amount-Principal(P)

∴ I = (300-100)Rs.

=Rs.200

and ∵ I = (P×R×T)/100

∴ 200 = (100×R×16)/100

⇒ 200 = (1600×R) /100

⇒ R = (200×100)/1600

⇒ R = 12.5%

In case 2 :

Amount = 4×principal

∴ A =( 4×100)Rs.

= Rs. 400

∵ I = A-P

∴ I = (400-100)Rs.

=Rs. 300

Time =?

Rate = 12.5 % p.a(per annum OR per year)

∵ Time = (Interset × 100)/P ×R

∴ Time = (300 × 100)/(100 ×12.5)

⇒ Time = 24 Years