Final answer:
To find the difference in interest earned on each amount after 5 years, calculate the interest for each account separately. For Account 1, the future value is $9,532.77, and for Account 2, the future value is $9,063.20. The difference in interest earned is $469.57.
Step-by-step explanation:
To find the difference in interest earned on each amount after 5 years, we need to calculate the interest for each account separately.
Account 1:
Mark placed half of the money, which is $8,250, into an account with a 2.75% interest rate compounded daily. To find the future value after 5 years, we use the formula:
Future Value = Principal * (1 + (Rate / n))^(n * time)
where:
Principal = $8,250
Rate = 2.75% or 0.0275
n = 365 (since it is compounded daily)
time = 5 years
Plugging these values into the formula, we get:
Future Value = $8,250 * (1 + (0.0275 / 365))^(365 * 5) = $9,532.77
Account 2:
Mark placed the other half of the money, which is also $8,250, into a different account with the same interest rate, but compounded monthly. To find the future value after 5 years, we use the same formula:
Future Value = Principal * (1 + (Rate / n))^(n * time)
where:
Principal = $8,250
Rate = 2.75% or 0.0275
n = 12 (since it is compounded monthly)
time = 5 years
Plugging these values into the formula, we get:
Future Value = $8,250 * (1 + (0.0275 / 12))^(12 * 5)
= $9,063.20
To find the difference in interest earned on each amount, we subtract the principal from the future value for each account:
Difference in interest = Future Value of Account 1 - Principal of Account 1
= $9,532.77 - $8,250
= $1,282.77
Difference in interest = Future Value of Account 2 - Principal of Account 2
= $9,063.20 - $8,250
= $813.20
The difference in interest earned on each amount after 5 years is $1,282.77 - $813.20 = $469.57