Final answer:
After calculating the compound interest for a $34,000 investment at 6% interest compounded annually for 9 years, the total amount would be approximately $57,442.26, with the interest earned at about $23,442.26. The closest provided option to this result is A) $23,144 in interest; $57,144 total.
Step-by-step explanation:
Calculating Compound Interest
To find out how much interest a person would earn on a $34,000 investment at 6% interest compounded annually for 9 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In this case, P = $34,000, r = 6% or 0.06, n = 1 (since it is compounded annually), and t = 9.
Plugging the numbers into the formula:
A = $34,000(1 + 0.06/1)^(1*9)
A = $34,000(1 + 0.06)^9
A = $34,000(1.06)^9
A = $34,000 * 1.6894781
A ≈ $57,442.26
The total interest earned is the final amount minus the original principal:
Interest = A - P
Interest ≈ $57,442.26 - $34,000
Interest ≈ $23,442.26
So, the total amount at the end of 9 years would be approximately $57,442.26, with the interest earned being about $23,442.26. Therefore, the closest answer from the provided options is A) $23,144 in interest; $57,144 total, although the exact calculation gives us a slightly different figure.