How much must be deposited now, at 6% interest compounded semiannually, to yield an annuity payment of $4000 at the end of each six month period, for a total of five years?

To find out how much must be deposited now, we need to use the present value of an annuity formula.

The present value of an annuity formula is given by:

PV = P * (1 - (1 + r/n)^(-n*t)) / (r/n)

Where:
PV is the present value of the annuity (the amount that must be deposited now),
P is the annuity payment,
r is the annual interest rate,
n is the number of compounding periods per year,
and t is the total number of years.

In this case we have:
P = $4000 (annuity payment)
r = 6% (annual interest rate)
n = 2 (compounded semiannually)
t = 5 (total number of years)

Plugging in these values into the formula, we can calculate the present value:

PV = 4000 * (1 - (1 + 0.06/2)^(-2*5)) / (0.06/2)

Simplifying the equation:

PV = 4000 * (1 - (1 + 0.03)^(-10)) / 0.03

Now we can solve the equation to find the present value (amount to be deposited now).