A principal of $2500 is invested at 6% interest, compounded annually. How many years will it take to accumulate $5000 or more in the account?

To solve this problem, we can use the formula for compound interest, which is:

A = P (1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years

In this case, we are trying to find out the time 't', so we will need to rearrange the formula to solve for 't'.

Given: P = $2500 A =$5000 r = 6% or 0.06 (in decimal) n = 1 (since the interest is compounded annually)

Substitute the given values into the formula:

5000 = 2500 (1 + 0.06/1)^(1*t)

Simplify the equation:

2 = (1.06)^t

To solve for 't', we will take the natural logarithm (ln) of both sides:

ln(2) = t * ln(1.06)

Now, divide both sides by ln(1.06) to solve for 't':

t = ln(2) / ln(1.06)

Using a calculator, you find that ln(2) is approximately 0.6931 and ln(1.06) is approximately 0.0583.

t = 0.6931 / 0.0583 ≈ 11.89 years

So, it will take approximately 12 years for the investment to accumulate to $5000 or more.