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

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

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.

To determine how long it will take for $100.00 to grow to $1000.00 when compounded daily at a rate of 1.5%, we can use the formula for compound interest:

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

Where:
A = the future value of the investment ($1000.00)
P = the principal amount ($100.00)
r = the annual interest rate (1.5% or 0.015 as a decimal)
n = the number of times the interest is compounded per year (365 for daily compounding)
t = the number of years

We need to solve for t. Rearranging the formula, we have:

t = (log(A/P)) / (n * log(1 + r/n))

Now, let's substitute the given values into the formula:

t = (log(1000/100)) / (365 * log(1 + 0.015/365))

Using a calculator or computer program, we can evaluate this equation to find t, which represents the number of years it will take for the initial amount of $100.00 to grow to $1000.00 when compounded daily at a rate of 1.5%.