Final answer:
It will approximately take 75.65 years for $396 to grow to $30,001 at a 4.40 percent annual compound interest rate, based on the formula for compound interest and solving for the variable that represents time.
Step-by-step explanation:
To determine how many years it will take for $396 to grow to $30,001 when invested at a 4.40 percent rate, compounded annually, we can use the compound interest formula which is shown below:
A = P(1 + r/n)nt
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time in years.
We want to solve for t when A is $30,001, P is $396, r is 0.044 (4.40%), and n is 1 since the interest is compounded annually. The equation becomes:
30,001 = 396(1 + 0.044/1)1*t
Solving for t, we get:
t = log(A/P) / (n*log(1 + r/n))
t = log(30,001/396) / log(1 + 0.044)
t ≈ 75.65
Therefore, it will take approximately 75.65 years for $396 to grow to $30,001 at a 4.40 percent annual compound interest rate.