Final answer:
The value of the annuity 6 months before the 1st payment is approximately ${{1600*(1-(1+0.06)^-20)/0.06}}.
Step-by-step explanation:
An annuity is a series of periodic payments or withdrawals of equal amounts. In this case, there are 20 payments of $200 made semiannually. The interest rate is 12% compounded semiannually.
To find the value of the annuity 6 months before the 1st payment, we need to calculate the present value of the annuity. The present value formula for an annuity is given by:
PV = (PMT / (1 + r)^n) * ((1 + r)^n - 1) / r
Where:
- PV is the present value of the annuity
- PMT is the amount of each payment ($200 in this case)
- r is the interest rate per period (12% per period in this case)
- n is the total number of periods (20 in this case)
Substituting the given values into the formula, we can calculate the present value: PV = ($200 / (1 + 0.06)^20) * ((1 + 0.06)^20 - 1) / 0.06 = ${{1600*(1-(1+0.06)^-20)/0.06}}.
Therefore, the value of the annuity 6 months before the 1st payment is approximately ${{1600*(1-(1+0.06)^-20)/0.06}}.