Final answer:
The future value of an investment of $13,000 at an annual interest rate of 4.5% compounded annually for 30 years is approximately $42,159, when calculated using the compound interest formula.
Step-by-step explanation:
To find the future value of $13,000 invested at 4.5% for 30 years compounded annually, we use the compound interest formula:
A = P(1 + r/n)nt
In this case:
- P (principal) = $13,000
- r (annual interest rate) = 4.5% or 0.045
- n (number of times interest applied per time period) = 1 (since it's compounded annually)
- t (number of time periods the money is invested) = 30 years
Now, we substitute these values into the compound interest formula to calculate the future value:
A = 13,000(1 + 0.045/1)1*30
A = 13,000(1 + 0.045)30
A = 13,000(1.045)30
Using a calculator:
A ≈ 13,000(3.243)
A ≈ $42,159
Therefore, the future value of $13,000 invested at 4.5% for 30 years, compounded annually, is approximately $42,159 (rounded to the nearest cent).