You invest one cent into an account offering 100 percent ann

You invest one cent into an account offering 100 percent annual interest. It is compounded weekly. How much time will it take for that one cent to grow into $1?

Solution

A=P(1+(r/n))^nt

compunded weekly=> n=52

A=1$=100cents

P=1 cent

r=100%=1

100=1(1+(1/52))^52t

100=(1.01923)^52t

52t =(ln100)/(ln1.01923)

t =(1/52)[(ln100)/(ln1.01923)]

t =4.65 years

it takes 4.65 years for that one cent to grow into $1