Final answer:
To calculate the time required to save $6,500 with monthly deposits of $290 at a 3.3% annual interest rate compounded monthly, the student needs to use and rearrange the future value for an annuity formula. Applying the specific values to the formula will yield the number of periods, which then must be divided by 12 to convert to years.
Step-by-step explanation:
The student wants to know how long it will take to save $6,500 at a rate of $290 per month with an annual interest rate of 3.3% compounded monthly. This is a question that involves the future value for an annuity formula, which is used to calculate the future value of a series of equal deposits made at regular intervals. To calculate the number of periods (months) needed to reach the goal of $6,500, we would use the following formula:
Future Value of Annuity (FV) = Pmt × × rac{((1 + r)^nt - 1)}{r}
Where Pmt is the regular payment amount, r is the interest rate per period, and nt is the total number of compounds over time (n is the number of times that interest is compounded per unit t).
We rearrange the formula to solve for nt (total number of periods) as follows:
nt = × rac{× ln(FV / Pmt + 1)}{× ln(1 + r)}
Since the question does not require a direct computation but instead asks to categorize the topic and grade level, we will not perform the calculation here. However, the student should apply the formula with the specific values for Pmt ($290), the monthly interest rate (3.3% annually compounded monthly would be 0.033/12 per month), and the desired future value ($6,500) to determine nt, and then divide by 12 to convert the number of periods to years, getting the time needed to buy a boat. By understanding the principles of compound interest, the student will be able to make informed decisions about their savings strategy.