A certificate of deposit is purchased for $5000 and held for 7 years. If the certificate earns 6% per annum, compounded quarterly, (four times per year) what is it worth at the end of the 7 years?

To solve this problem, we will 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 = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

Given in the problem: P = $5000 r = 6% or 0.06 (in decimal) n = 4 (since it's compounded quarterly) t = 7 years

Substituting these values into the formula:

A = 5000 (1 + 0.06/4)^(4*7)

Now, calculate the expression inside the parenthesis:

= 5000 (1 + 0.015)^28

= 5000 * (1.015)^28

Now, calculate the power:

= 5000 * 1.488864

Finally, multiply the principal amount by the calculated value:

A = $7444.32

So, the certificate of deposit is worth $7444.32 at the end of the 7 years.