Final answer:
To find the principal, you can use the formula for compound interest. The principal should be approximately $30,157.40.
Step-by-step explanation:
To find the principal, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment (which in this case is $45,000)
P is the principal
r is the annual interest rate (which is 5% or 0.05)
n is the number of times interest is compounded per year (monthly compounding means n = 12)
t is the number of years
Using the given values, we have:
45000 = P(1 + 0.05/12)^(12*10)
Solving for P:
P = 45000 / (1 + 0.05/12)^(12*10)
P = 45000 / (1.00416667)^(120)
P ≈ 30157.40
Therefore, Bill must have a principal of approximately $30,157.40.