Lights, Camera, and More sells filmmaking equipment. The company offers three purchase options: $(1)$ pay full cash today, $(2)$ pay one$-$half down and the remaining one$-$half plus $10\%$ in one year, or $(3)$ pay nothing down and the full amount plus $15\%$ in one year. George is considering buying equipment from Lights, Camera, and More for $$130,000$ and therefore has the following payment options:

Payment Today Payment in One Year Total Payment

Option $1$ $$130,000$ $ $0$ $$130,000$

Option $265,00071,500136,500$

Option $30149,500149,500$

Required:

$1-$a$.$ Assuming an annual discount rate of $12\%,$ calculate the present value and the total cost.

$1-$b$.$ Which option's cost has the lowest present value?