Answer:Comparing the amounts, we see that Dominic will have more money accrued in his account than Agatha. Dominic will have approximately $950.18 while Agatha will have $923.80.
Step-by-step explanation:
Agatha invested $775 into a simple interest bearing account at a rate of 2.4% for 8 years, while Dominic invested the same amount into an account that is compounded quarterly at the same rate for 6 years.
To compare who will have more money accrued in their account, let's calculate the amount of money each person will have at the end of their respective investment periods.
For Agatha's simple interest account, we can use the formula for simple interest:
Interest = Principal * Rate * Time
In this case, the principal (amount invested) is $775, the rate is 2.4%, and the time is 8 years.
Interest = 775 * 0.024 * 8 = $148.80
So, after 8 years, Agatha will have earned $148.80 in interest.
To find the total amount in Agatha's account, we add the interest to the principal:
Total amount in Agatha's account = Principal + Interest = 775 + 148.80 = $923.80
Now, let's calculate the amount in Dominic's compounded quarterly account. For compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accrued
P = principal
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal is $775, the annual interest rate is 2.4% (or 0.024 as a decimal), the interest is compounded quarterly (so n = 4), and the time is 6 years.
A = 775(1 + 0.024/4)^(4 * 6)
Using a calculator or simplifying the equation step by step, we find that:
A ≈ $950.18
Therefore, after 6 years, Dominic will have approximately $950.18 in his account.
Comparing the amounts, we see that Dominic will have more money accrued in his account than Agatha. Dominic will have approximately $950.18 while Agatha will have $923.80.
I HOPE THATS HELPFUL:)))))))