Final answer:
Bank Y (which holds annuity Y) will have more money in 16 years with a total of $9,631.55, compared to Bank Z (which holds annuity Z) with a total of $4,706.09.
Step-by-step explanation:
To determine which account will have more money in 16 years, we need to calculate the future value of each annuity using compound interest. Annuity Y begins in 2 years and pays $500 for each year for 7 years, while annuity Z begins in 8 years and pays $500 each year for 7 years.
Let's first calculate the future value of annuity Y. Since annuity Y begins in 2 years, we will use 14 years as the time period for compounding. Assuming a positive interest rate, let's say 5%, the future value of annuity Y can be calculated using the formula:
Future Value = Payment x [(1 + Interest Rate)^Time - 1] / Interest Rate
Plugging in the values, we have: Future Value of Annuity Y = $500 x [(1 + 0.05)^14 - 1] / 0.05 = $9,631.55
Now, let's calculate the future value of annuity Z. Since annuity Z begins in 8 years, we will use 8 years as the time period for compounding. Using the same interest rate of 5%, we can calculate the future value of annuity Z:
Future Value = Payment x [(1 + Interest Rate)^Time - 1] / Interest Rate
Plugging in the values, we have: Future Value of Annuity Z = $500 x [(1 + 0.05)^8 - 1] / 0.05 = $4,706.09
Therefore, in 16 years, Bank Y (which holds annuity Y) will have more money with a total of $9,631.55 compared to Bank Z (which holds annuity Z) with a total of $4,706.09.