Okay, let's calculate the interest earned by each person over 6.5 years.
Jack's account earns annual simple interest, so the formula for simple interest is:
I = P * r * t
where:
I = interest earned
P = principal (initial amount deposited)
r = annual interest rate
t = time in years
Using the given values, we get:
I = 17,250 * 0.06 * 6.5
I = $6,332.50
Therefore, Jack will earn $6,332.50 in simple interest over 6.5 years.
Carlie's account earns annual compound interest, so the formula for compound interest is:
A = P * (1 + r/n)^(n*t)
where:
A = amount after time t
P = principal (initial amount deposited)
r = annual interest rate
n = number of times interest is compounded per year
t = time in years
Using the given values, we get:
A = 17,250 * (1 + 0.06/1)^(1*6.5)
A = $27,943.93
The amount after 6.5 years is $27,943.93, which includes the principal and compound interest earned. To find the amount of interest earned, we subtract the principal:
Interest earned = A - P = $27,943.93 - $17,250 = $10,693.93
Therefore, Carlie will earn $10,693.93 in compound interest over 6.5 years.
So, Carlie will earn more interest than Jack, and the difference between the interest earned is:
$10,693.93 - $6,332.50 = $4,361.43
Therefore, Carlie will earn $4,361.43 more interest than Jack over 6.5 years.