Final answer:
Using the compound interest formula, it would take approximately 14 years for Molly's investment to grow to $12,000 at an annual interest rate of 2% compounded weekly. This result is not within the provided multiple choice options, so there may be an error in the question or answers.
Step-by-step explanation:
To determine how many years it will take for Molly's $8,700 investment to grow to $12,000 with an annual interest rate of 2% compounded weekly, we use the formula for compound interest:
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 the money is invested for in years.
In this case, P = $8,700, A = $12,000, r = 0.02, n = 52, and we are solving for t. After rearranging the formula and solving for t, we get:
t = log(A/P) / (n*log(1+r/n))
Plugging the values into the formula, we calculate the time t.
t = log(12000/8700) / (52*log(1+0.02/52))
t ≈ 14.2047
Therefore, it would take approximately 14 years for the investment to grow to $12,000, which is not an option in the multiple-choice answers provided. However, this result is clearly beyond the range of the given options (5, 8, 10, 12 years), indicating that an error may have been made in formulating the question or the given answer options.