Your firm is considering the purchase of a new office phone system. You can either pay $$$$31$ comma $500$now$,$ or $$$$1$ comma $050$ per month for $42$ months.

a$.$ Suppose your firm currently borrows at a rate of $7\%$ per year$($APR with monthly$$ compounding$).$ Which payment plan is more$$ attractive?

b$.$ Suppose your firm currently borrows at a rate of $20\%$ per year$($APR with monthly$$ compounding$).$ Which payment plan would be more attractive in this$$ case?

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Part $1$

a$.$ Suppose your firm currently borrows at a rate of $7\%$ per year$($APR with monthly$$ compounding$).$ Which payment plan is more$$ attractive?

The present value of the monthly cash flows is $$$