Final answer:
Joe will reach his goal of earning $2,000 in interest by the age of 16 as his investment will grow to $10,100 in four years due to compound interest, earning him $2,100 in interest.
Step-by-step explanation:
To determine if Joe will reach his goal of earning $2,000 in interest by the time he is 16, we need to calculate the future value of his $8,000 investment at a 6% annual interest rate over four years. Using the formula for compound interest, the future value FV is calculated as:
FV = P (1 + r)n
Where P is the principal amount ($8,000), r is the annual interest rate (6% or 0.06), and n is the number of years (4).
Plugging in the values we get:
FV = $8,000 (1 + 0.06)4
FV = $8,000 (1.2625)
FV = $10,100
This means that in four years, Joe will have $10,100 in his account. To calculate the interest earned, we subtract the original principal from the future value:
Interest Earned = FV - P
Interest Earned = $10,100 - $8,000
Interest Earned = $2,100
Since Joe's interest earned is $2,100, which is more than his goal of $2,000, he will indeed reach his goal before he turns 16.