Answer:
a-1) Present value of the instalment option = $93.08
Present value of paying the bill immediately =$90
a2) Paying the bill immediately is the better deal
b-1) Present value of the instalment option = $88.65
b-2) Paying in instalments in this case is the better deal
Explanation:
a-1) Calculate Present value of the instalment option
The payments are spread out as follows: $25 immediately, and 25 at the end of each of the following 3 years, this is an annuity due where the present value is calculated as follows:
![Present value =PMT*\frac{[1-(1+i)^-^n]}{i}*(1+i)](https://tex.z-dn.net/?f=%20Present%20value%20%3DPMT%2A%5Cfrac%7B%5B1-%281%2Bi%29%5E-%5En%5D%7D%7Bi%7D%2A%281%2Bi%29)
PMT = the annuity payment at the beginning of each period=$25
i = interest rate per period that would be compounded for each period
=0.05
n = number of payment periods=4
Present value =
=$93.08
Present value of paying the bill immediately= $100 less the 10% discount= $100*0.9 = $90
a-2)Paying the bill immediately is the better deal as it has a lower cost of $90 compared to paying in instalments which a present value cost of $93.08
b1) If the payments on the 4-year instalment plan do not start for a full year, then the present value of the payment stream is calculated as follows:
![Present value =PMT*\frac{[1-(1+i)^-^n]}{i}*\frac{(1+i)}{1+1}](https://tex.z-dn.net/?f=%20Present%20value%20%3DPMT%2A%5Cfrac%7B%5B1-%281%2Bi%29%5E-%5En%5D%7D%7Bi%7D%2A%5Cfrac%7B%281%2Bi%29%7D%7B1%2B1%7D)
= ![PMT*\frac{[1-(1+i)^-^n]}{i}](https://tex.z-dn.net/?f=PMT%2A%5Cfrac%7B%5B1-%281%2Bi%29%5E-%5En%5D%7D%7Bi%7D)
=
= 88.65
b-2) paying in instalments in this case is the better deal as it has a lower cost of $88.65 compared to paying the bill immediately which has present value cost of $90.