Answer:
We can use the formula for compound interest to solve this problem.
Formula: FV = PV*(1 + r/n)^(n*t)
Where:
FV = future value
PV = present value
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)
In this problem, we are given:
PV = $10,000
FV = $2,000,000
t = 40 years
n = 12 (monthly compounding)
We need to find the minimum annual interest rate (r) required to reach the future value of $2,000,000.
We can rearrange the formula to solve for r:
r = n*((FV/PV)^(1/(n*t))) - n
Substituting the given values:
r = 12*((2,000,000/10,000)^(1/(12*40))) - 12
Simplifying:
r = 0.0874 or 8.74%
Therefore, the stated annual rate must be at least 8.74% to achieve a future value of $2,000,000 in 40 years with a $10,000 deposit and monthly compounding.