Question

If a certain sum becomes double in 3 years at certain rate of interest at C.I. Then in how many years it will become 16 times?

Answer 1

Answer:

formula used n1^t2=n2^t1

3 years= 2 times

& ?=16 times

here n1=2

n2=16

t1=3years

t2=?

after solve we get 12 year

Answer 2

The answer is 12 years.

GIVEN

If a certain sum becomes double in 3 years at certain rate of interest at C.I.

TO FIND

Time it will become 16 times.

SOLUTION

Let the principal amount be P

And,

Rate interest = R%

It is given that The pricipal gets doubled in 3 years

So,

Amount = 2P

Applying the formula,

$A = p (1 + \frac{r}{100} )^{t}$

Where,

A = Final amount

p = Principal balance

r = rate%

n = number of times rate % is applied.

t = time period.

Therefore,

$2P = P (1 + \frac{r}{100} )^{3}$

$2 = P(1 + \frac{r}{100} )^{3}$

(Equation 1)

Let the principal amount becomes 16 times of initial amount in t times;

$16P = P (1 + \frac{r}{100} )^{t}$

$16 = P (1 + \frac{r}{100} )^{t}$

(Equation 2)

Now,

Exponentiating LHS of Equation 1 by 4

SO,

LHS of Equation 1 = LHS of Equation 2

So,

RHS of Equation 1 = RHS of Equation 2

Therefore,

t = 3 × 4

t = 12 years.

Hence, The answer is 12 years.

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