Question

2. (This question is based on actual data, but l've changed numbers slightly, and converted monthly payments to yearly, for simplicity). The Brick sells a sofa at a price of $2,520. Alternatively, you can agree to pay $840 at the beginning of each year for three years, starting today; in addition, if you choose to pay in installments, you must pay an upfront "administration fee" of $150. If you face an interest rate of 4%, are you better of buying the sofa upfront or paying in installments (plus the admin fee)?

Answer 1

In case of full upfront payment,

PV of cost of full upfront payment=$2520

In case of installments,

PV of cost in case of installments=150+840*(P/A,0.04,3)*(1+0.04)

(It is a case of annuity due as payments are made at the beginning of year)

We know that

(1+i)" (P/A, i,n)=-

1-1+0.04): (Ρ/Α, 0.04, 3) = 2.775091 0.04

PV of cost in case of installments=150+840*2.775091*(1+0.04)=$2574.32

We can see that PV of cost of paying with installments (incl administration fee) is higher. It is not advisable to buy on installment option. So, I would be better of buying sofa by paying full upfront price.