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Joe, who is 12, has $8,000 in a bank account that pays a 6% annual interest rate. He wants to earn $2,000 in interest by the time he is 16. If he leaves his money in this bank account, will he reach his goal?

User HGen
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1 Answer

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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.

User Jden
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