Question

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?

Answer 1

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:

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

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

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

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

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