Final answer:
The interest on a $34,000 investment at 6% interest compounded quarterly for 9 years is approximately $20,364, with the total amounting to $54,364. The formula for compound interest is used to calculate the final amount and then subtract the principal to find the interest earned. Option D is the correct choice.
Step-by-step explanation:
The question is about calculating the interest earned on a $34,000 investment with a 6% interest rate compounded quarterly for a duration of 9 years. To find the interest and the total amount at the end of the period, we 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 ($34,000).
- 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.
Given:
- P = $34,000
- r = 6% or 0.06
- n = 4 (quarterly compounding)
- t = 9 years
Plugging the values into the formula:
A = 34000(1 + 0.06/4)^(4*9)
A = 34000(1 + 0.015)^(36)
A = 34000(1.015)^36
A ≈ $54,364
To find the interest earned:
Interest = A - P
Interest = $54,364 - $34,000
Interest ≈ $20,364
The correct option from the given choices that represents the interest earned and the total amount at the end of 9 years is Option D: $20,364 in interest; $54,364 total.