$4-56$ Consider the following cash flow:

Alice was asked to compute the value of $P$ for

the cash flow at $8\%$ interest, assuming the net

present value of the cash flows is zero. She

wrote three equations:

$(1)P=1,000(\frac{P}{A},8\%,8)-150(\frac{P}{G},8\%,8)$

$+150(\frac{P}{G},8\%,4)(\frac{P}{F},8\%,4)$

$(2)P=400(\frac{P}{A},8\%,8)+600(\frac{P}{A},8\%,5)$

$-150(\frac{P}{G},8\%,4)$

$(3)P=150(\frac{P}{G},8\%,4)+850(\frac{P}{A},8\%,4)$

$+400(\frac{P}{A},8\%,4)(\frac{P}{F},8\%,4)$

Which of the equations is correct?