Question

If $13,000 is invested at 4.5% for 30 years, find the future value if the interest is compounded the following ways. (round your answers to the nearest cent.)

(a) annually

Answer 1

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).