To calculate the time it takes for an investment to reach a specific amount, we can use the continuous compound interest formula: A = P * e^(rt), where A is the final amount, P is the principal investment, r is the interest rate, and t is the time in years.
In this case, your principal investment is $1000, the interest rate is 10% (or 0.10), and you want to reach $1 million.
We can rearrange the formula to solve for t: t = ln(A/P) / r
Plugging in the values, we have:
t = ln(1000000/1000) / 0.10
Calculating this equation, we find:
t ≈ ln(1000) / 0.10 ≈ 6.9078 / 0.10 ≈ 69.08 years
Therefore, it will take approximately 69 years to become a millionaire with a $1000 investment at 10% interest compounded continuously.