Question

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?

Answer 1

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.

Step-by-step 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