Oriole Incorporated management is considering investing in two alternative production systems. The systems are mutually exclusive, and the cost of the new equipment and the resulting cash flows are shown in the accompanying table. The firm uses a $7$ percent discount rate for their production systems.

Year

System $1$

System $2$

$-$$$15,000$

$-$$$42,200$

$1$

$15,000$

$34\mathrm{.}800$

$2$

$15\mathrm{.}000$

$34,800$

$3$

$15,000$

$34,800$

What are the payback periods for production systems $1$ and $2?$