Final Answer:
a) The final amount after 8 years is $63,584.11.
b) The total interest earned on the original investment is $24,584.11.
Explanation:
To find the final amount after 8 years, the formula for compound interest A = P(1 + r/n)^(nt) is used. Here, P is the principal amount ($39,000), r is the annual interest rate (7.5% or 0.075), n is the number of times interest is compounded per year (compounded annually, so n = 1), and t is the time the money is invested for (8 years).
Substituting these values into the formula, A = $39,000 * (1 + 0.075/1)^(1*8), we get A ≈ $63,584.11.
To calculate the total interest earned, subtract the original principal from the final amount: $63,584.11 - $39,000 = $24,584.11.
Compound interest enables the original investment of $39,000 to grow to $63,584.11 after 8 years, with $24,584.11 as the total interest earned on the initial investment.
Compound interest is a powerful concept in finance, where the interest not only earns on the initial principal but also on the accumulated interest over time, leading to exponential growth. Understanding how different variables—such as the principal, interest rate, compounding frequency, and time—affect the final amount aids in making informed financial decisions.