Question

A sum of money at compound interrest doubles itself in 5 years. In how many years, it would amount to 8 times of itself at the same rate of interest ?

Answer 1

let r is the rate of compound interest
now ,
in first case:-
2p=p (1+r/100)^5
2=(1+r/100)^5
take log both side
log2=5log (1+r/100)
log (1+r/100)=log2/5 --------------(1)


in second case:-
8p=p(1+r/100)^n
8=(1+r/100)^n
take log both side
log8=2log2=nlog (1+r/100)
put equation (1)
2log2=nlog2 / 5
10= n
hence 10 years