How much money must be deposited now, at 6% interest compounded semiannually, to yield an annunity payment of $4000 at the end of each six month period, for a totl of five years? Round to the nearest cent
To calculate the amount of money that must be deposited now, we need to use the formula for the present value of an annuity. The formula is:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV is the present value (the amount of money to be deposited now),
PMT is the annuity payment ($4000 in this case),
r is the interest rate per period (6% divided by 2, since it's compounded semiannually),
n is the total number of periods (5 years times 2, since it's compounded semiannually).
Plugging in the values, we can calculate the present value:
PV = 4000 * (1 - (1 + (0.06/2))^(-5*2)) / (0.06/2)
PV ≈ $34,633.36
Therefore, approximately $34,633.36 must be deposited now to yield an annuity payment of $4000 at the end of each six-month period, for a total of five years.