How much must you deposit in an account

that pays 6% semi-annual interest, compounded annually, to have a balance of $9000 in 15 years?
I'm stuck with this question, please explain the steps for the answer.

Are you sure it is not 6% annual compounded semi-annually ?

No Idea, the question completely asks that. I was thinking about 12% annually compounded, but the answer I got was wrong due to Solve and Check.

15 years is 30 periods each 3% or multiply by 1.03 every six months

9000 = d * 1.03^30
9000 = 2.427262471 d
d = $ 3,707.88

12% is way high and no one expresses compounding annually with semi annual interest rate. Typo in your book I suspect.

To find the amount that you must deposit in the account, you need to use the formula for compound interest:

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

Where:
A is the future value of the account (in this case, $9000)
P is the principal amount (the amount you need to find)
r is the interest rate per period (6% or 0.06)
n is the number of times interest is compounded per year (in this case, once since it is compounded annually)
t is the number of years (15 in this case)

Now, let's calculate it step by step:

First, plug in the given values into the formula:

9000 = P(1 + 0.06/1)^(1*15)

Next, simplify the equation:

9000 = P(1.06)^15

To find the actual value of P, you need to isolate it on one side of the equation. Divide both sides of the equation by (1.06)^15:

P = 9000 / (1.06)^15

Using a calculator or spreadsheet, calculate (1.06)^15, which is approximately 2.4395:

P = 9000 / 2.4395

Finally, calculate the value of P:

P ≈ $3690.44

Therefore, you must deposit approximately $3690.44 in the account to have a balance of $9000 after 15 years.