Question

a sum of money placed at C.I. double itself in 4 yrs. Calculate the time taken to amount it 8 times.​

Answer 1

Given :-

• Sum of money becomes 2 times in 4 years.
• Rate is compounded Annually.

To Find :-

• in how many years it will be 8 Times. ?

Solution :-

Let ,

→ Principal = P

→ Rate % = R

→ Time = 4 years .

→ Amount = 2P

So,

→ P [ 1 + (R/100) ]⁴ = 2P

→ [1 + (R/100) ]⁴ = 2 ------------------- Equation (1).

________________

Now, Let it becomes 8 times in T years.

So,

→ P [ 1 + (R/100) ]^T = 8P

→ [ 1 + (R/100) ]^T = 8

→ [ 1 + (R/100) ]^T = (2)³

Now, Putting value of 2 from Equation (1) Here , we get,

→ [ 1 + (R/100) ]^T = { [ 1 + (R/100) ]⁴}³

→ [ 1 + (R/100) ]^T = [ 1 + (R/100) ]^12

Now, we know that, if a^b = a^c Than, b = c,

So,

→ T = 12 Years (Ans).

Hence, The Sum of Money will be 8 Times in 12 years.

_______________