Question

A sum of money doubles it self in 7 years. In how many years will it become four fold​

Answer 1

If compound interest is used, then, as per the question, in 7 years

A=2P

⟹P{1+R100}7=2P

⟹{1+R100}7=2

⟹{1+R100}=217 ....(1)

Now, for the principal to quadruple,

A=4P

⟹P{1+R100}t=4P

⟹{1+R100}t=4

Now substituting (1) in the above expression we get,

{217}t=4

⟹2t7=4

Taking log of both sides, we get

t7×log(2)=log(4)

⟹t7=log(4)log(2)=2

⟹t=2×7=14 years (which is quite intuitive)

Where,

P = principal

R = rate of interest (p.a.)

t = time (years)

A = amount