Final answer:
To determine the time required for an account to grow from $475 to $1545 with an interest rate of 6.8% compounded monthly, the compound interest formula is used to solve for time (t). After substituting the given values into the formula t = log(A/P) / (12 * log(1 + r/n)), it is found that it will take approximately 14.24 years for the account to reach the desired amount.
Step-by-step explanation:
To determine how long it will take for the account to grow from $475 to $1545 with an interest rate of 6.8% compounded monthly, we can use the compound interest formula:
A = P(1 + r/n)nt
Here, 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, and t is the time in years.
Rewriting the formula to solve for t, we get:
t = log(A/P) / (n * log(1 + r/n))
Substituting the given values:
P = $475
A = $1545
r = 6.8% or 0.068
n = 12 (since the interest is compounded monthly)
Using these values, we calculate t as follows:
t = log(1545/475) / (12 * log(1 + 0.068/12))
Calculating the above expression using a calculator:
t ≈ 14.24 years
Therefore, it will take approximately 14.24 years for the account to contain $1545.