To calculate the interest earned after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal (initial amount invested)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this case, Jackson invested $8,000 at an annual interest rate of 4.5% compounded annually for 3 years. Plugging in the values, we get:
A = 8,000(1 + 0.045/1)^(1*3)
A = 8,000(1.1401)
A = 9,120.80
The final amount after 3 years is $9,120.80. To find the interest earned, we subtract the initial amount invested from the final amount:
Interest earned = $9,120.80 - $8,000
Interest earned = $1,120.80
Therefore, Jackson will have earned $1,120.80 in interest after 3 years.