Question

show that a sum of money will increase more than 100times in 100 years at 5% compound interest .

Answer 1

let p is the sum

use A=p(1+r/100)^n

given,
r=5%
n=100 years
A=p(1+5/100)^100
=p(1+0.05)^100
=p(1.05)^100

hence
A=p(1.05)^100
take log both side

logA=logp(1.05)^100
=logp+ 100log(1.05)
=logp +100(0.021)
=logp+2.1 ------------(1)
S=100p
take log both side
logS=log(100p)
=logp +log(10)^2
=logp +2 -------------(2)
you can see equation (1) and (2)
logA>logS
hence,
A>S
so,
we can say that money will increase more then 100yimes in 100years at 5% in compound interest