Answer:

To find the interest rate needed for a principal of $4,000 to increase to $4,500 in 10 years, we can use the formula:

A = P(1 + r)^n

Where A is the final amount, P is the principal, r is the interest rate, and n is the number of years.

In this case, we know that:

A = $4,500

P = $4,000

n = 10

So we can set up the equation as:

$4,500 = $4,000(1 + r)^10

To solve for r, we can divide both sides by $4,000:

$4,500/$4,000 = (1 + r)^10

1.125 = (1 + r)^10

We can find the interest rate by taking the 10th root of 1.125, and then subtracting 1.

r = (1.125)^(1/10) - 1

r = 0.059

So the interest rate needed for a principal of $4,000 to increase to $4,500 in 10 years, compounded annually, is 5.9%

Step-by-step explanation: