Final answer:
To find how long it will take to grow $259 to $599 at 6% APR compounded monthly, we use the compound interest formula A = P(1 + r/n)^(nt). We plug in the given values and solve for 't', the time in years, which may involve using logarithmic functions or a calculator. Since this is a multiple-choice question, test each option with the formula to find the correct answer.
Step-by-step explanation:
To determine how long it will take to turn an initial investment of $259 into $599 with an account that pays 6% APR interest compounded monthly, we need to use the formula for compound interest:
A = P(1 + rac{r}{n})^{nt}
Where:
Here, we have:
Plugging these values into the formula, we get:
$599 = $259(1 + rac{0.06}{12})^{12t}
We now need to solve for t, the time in years. However, this requires logarithmic functions to isolate t, and the exact value will likely need to be calculated using a calculator or logarithmic tables.
Since the question presents multiple choice answers, one could plug in the given time frames (4, 8, 12, and 16 months) into the formula to see which one results in an amount that is equal to or greater than $599 and determine the correct answer.