Final answer:
Sheila loses a future value of approximately $2688 in savings over 10 years due to out-of-network ATM fees of $2 per transaction, assuming a 3% annual compounding interest rate and 100 transactions per year.
Step-by-step explanation:
Sheila is faced with out-of-network ATM service fees, which will affect her savings over time. To find the future value of the money spent on ATM fees, one must consider the fees as a lost opportunity to earn interest at a 3% annual rate. Over 10 years, with 100 transactions each year at $2 per transaction, Sheila spends a total of $2000 on ATM fees (100 transactions x $2/transaction x 10 years).To calculate the future value of transactions made by Sheila on out-of-network ATMs, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the principal amount is $2 per transaction, the annual interest rate is 3%, n is 1 (since the interest is compounded annually), and t is 10 years. So the formula becomes:A = 2(1 + 0.03/1)^(1*10)Calculating this expression, we find that the future value of Sheila's transactions after 10 years is approximately $2.72. Rounded to the nearest dollar, the future value would be $3.To calculate the future value of this $2000 with an annual compounding interest rate of 3%, we use the future value formula:Future Value = Present Value x (1 + r)^nWhere r is the annual interest rate (expressed as a decimal) and n is the number of years.Future Value = $2000 x (1 + 0.03)^10Future Value = $2000 x (1.03)^10Future Value = $2000 x 1.343916379When calculated, the future value approximately equals $2687.83. Rounded to the nearest dollar, Sheila loses $2688 in potential savings over 10 years.