Final answer:
Eileen is paying $1080 per year in credit card finance charges. If invested at 4% interest instead, we would use the future value of an annuity formula to determine how long it would take to save $11,000. An exact number of years would require algebraic calculation or financial software.
Step-by-step explanation:
Eileen is currently paying a significant amount in finance charges on her credit card. If she redirected these payments towards saving for a car, assuming she is able to invest in an account with a 4% interest rate, we need to calculate how long it would take her to save $11,000.
To solve this problem, we will use the formula for the future value of an annuity, which is FV = Pmt * [(1 + r)^n - 1] / r, where Pmt is the annual payment, r is the annual interest rate, and n is the number of years. Here, Pmt is $1,080, r is 0.04 (4%), and we need to find n when FV is $11,000. This calculation requires a bit of algebra and might be easier to handle with a financial calculator or software capable of solving for n in this annuity equation.
Without an exact calculator or software, a rough estimate could be made by noting that without interest, Eileen would take a little over 10 years just to save the principal amount. Considering a 4% interest, it would be somewhat less than 10 years since the interest would help the balance grow each year. However, without an exact calculation, we cannot provide the precise number of years.