Answer:
a-1) Present value of the installment option is $93.08.
Present value for immediate bill payment is $90.
a2) Opting to pay the bill immediately is the preferable choice.
b-1) Present value of the installment option amounts to $88.65.
b-2) In this scenario, paying in installments is the better option.
Explanation:
a-1) To determine the present value of the installment plan, the payments occur as follows: $25 immediately, followed by $25 at the end of each of the next 3 years. This setup constitutes an annuity due, and the present value can be calculated as follows:
PMT denotes the annuity payment at the start of each period, which is $25.
i signifies the interest rate compounded per period.
=0.05
n represents the number of payment periods, which amounts to 4.
Present value = =$93.08
The present value of immediate bill payment equals $100, reduced by the 10% discount, calculated as $100 * 0.9 = $90.
a-2) Paying immediately is advantageous since it costs $90 compared to the $93.08 present value of installments.
b1) If the installment payments do not commence for another year, the present value of the payment series is computed as:
=
= = 88.65
b-2) In this instance, paying via installments is better as it is less expensive at $88.65 compared to the immediate payment's present value at $90.