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adelina 88
1 month ago
7

A store offers two payment plans. Under the installment plan, you pay 25% down and 25% of the purchase price in each of the next

3 years. If you pay the entire bill immediately, you can take a 10% discount from the purchase price. Assume the product sells for $100. a-1. Calculate the present value of the payments if you can borrow or lend funds at an interest rate of 5 percent. (Do not round intermediate calculations. Round your answer to 2 decimal places.) a-2 Which is a better deal? b-1. Calculate the present value if the payments on the 4-year installment plan do not start for a full year. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b-2. Which is a better deal?
Business
1 answer:
Katen [2.8K]1 month ago
4 0

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:

Present value =PMT*\frac{[1-(1+i)^-^n]}{i}*(1+i)

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 =25*\frac{[1-(1+0.05)^-^4]}{0.05}*(1+0.05) =$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:

Present value =PMT*\frac{[1-(1+i)^-^n]}{i}*\frac{(1+i)}{1+1}

                                          = PMT*\frac{[1-(1+i)^-^n]}{i}

                                          = 25*\frac{[1-(1+0.05)^-^4]}{0.05} = 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.

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