Your firm is considering the purchase of a new office phone system. You can either pay $ 32 comma 500 now, or $ 900 per month for 31 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 19 % per year (APR with monthly compounding). Which payment plan would be more attractive in this case?

Always the second option will be better because 31 payments x $900 = $27,900, no matter what interest rate you use, it cannot be negative.

Explanation:

A) two options:

$32,500 now or $900 in 31 months

to determine by how much the installment plan is is better, we need to determine the present value of the annuity:

present value = payment x {[1 - 1 / (1 + r) ⁿ] / r}

r = 7% / 12 = 0.58333% payment = $900 n = 31

present value = $900 x {[1 - 1 / (1 + 0.0058333) ³¹] / 0.0058333} = $25,455

with this plan you save = $32,500 - $25,455 = $7,045

B) if the interest rate is higher, you save even more money:

present value = payment x {[1 - 1 / (1 + r) ⁿ] / r}

r = 19% / 12 = 1.58333% payment = $900 n = 31

present value = $900 x {[1 - 1 / (1 + 0.0158333) ³¹] / 0.0158333} = $21,914

with this plan you save = $32,500 - $21,914 = $10,586