Question

an amount becomes 3 times in 6 years then in how many years it would be 27 times through Compounded interest and Simple interest respectively.​

Answer 1

Answer:

I think the answer is 9

Answer 2

Given:

An amount becomes 3 times in 6 years

To find:

The number of years in which it would be 27 times

Solution:

The number of years in which it would be 27 times through S.I. is 78 and through C.I. is 18.

We can find the years by following the given steps-

We know that number of years will be calculated differently for simple and compound interest.

i. through simple interest

The amount becomes 3 times of itself in 6 years.

So, let the number of years after which it will become 27 times be S.

We know that S=(Y-1)×T/(X-1)

Here X and Y are the number of times the amount has increased.

X=3 and Y=27 and T represent the number of years it took to be X times.

So, S=(27-1)×6/(3-1)

S=26×6/2

S=13×6

S=78 years

ii. through compound interest

The amount becomes 27 times in S.

Here, S=T×n and $X^{n}$=Y

On putting the values, we get

$3^{n}$=27

n=3

S=6×3

=18 years

Therefore, the number of years in which it would be 27 times through S.I. is 78 and through C.I. is 18.