Question

How long will it take for $100.00 compounded daily at 1.5 % to become $1000.00

Answer 1

interest rate per day = .015/365
= 4.11 * 10^-5
so
1000 = 100 * 1.0000411^n
n log 1.0000411 = log 10 = 1
n = 56030 days or 153 years

Answer 2

n=number of years

Daily interest=0.015/365
1000=100*(1+(0.015/365))^(n*365)
Take log on both sides
log(1000)=log(100)+(n*365)*log(1+0.015/365)

Solve for n.

It turns out that it takes only just over 150 years instead of 667 years for simple interest.

If we use the average of 365 1/4 days per year, it does not make a big difference. Try it.