Final answer:
To determine the amount in Sydney's and Benny's accounts after 10 and 20 years, we can use the future value formula for compound interest. Sydney had more money in the account after both 10 and 20 years. The future value functions for Sydney's and Benny's accounts can be written as separate equations.
Step-by-step explanation:
To determine the amount in Sydney's account after 10 years, we can use the future value formula for compound interest:
Future Value = P(1 + r/n)nt
Where P is the principal (initial amount invested), r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.
For Sydney, P = $100, r = 0.05, n = 12 (compounded monthly), and t = 10. Plugging these values into the formula, we get:
Future Value = 100(1 + 0.05/12)12*10
Calculating this gives us a future value of approximately $16,470.73 for Sydney's account after 10 years.
To determine the amount in Benny's account after 10 years using the same formula, we can plug in P = $80, r = 0.08, n = 12, and t = 10. Calculating this gives us a future value of approximately $16,168.69 for Benny's account.
Therefore, Sydney had more money in the account after 10 years.
For Sydney's account after 20 years, we can plug in P = $100, r = 0.05, n = 12, and t = 20. Calculating this gives us a future value of approximately $43,219.53.
For Benny's account after 20 years, we can plug in P = $80, r = 0.08, n = 12, and t = 20. Calculating this gives us a future value of approximately $41,933.20.
Therefore, Sydney still had more money in the account after 20 years.
The future value function for Sydney's account is: Future Value = P(1 + 0.05/12)12t
The future value function for Benny's account is: Future Value = P(1 + 0.08/12)12t