Question

You have just started your first job and you want to have the basic appliances (fridge, washer, dryer, etc.) in your apartment. You face the following choices: (i) Purchase all appliances at the store using a bank loan. There is no down payment as the bank can take your appliances if you default on the loan. The loan is at the annual market rate of 9%, and the loan amount is $8,400 to be repaid monthly over 4 years. (ii) Rent-to-buy from the same store. The monthly rental is $185 for 48 months and then you pay $800 to own all the appliances. What is the net cost today of the cheapest option? (Enter just the number in dollars without the $ sign or a comma and round off decimals to the closest integer, i.e., rounding $30.49 down to $30 and rounding $30.50 up to $31.)

Answer 1

You can only compare "monies" if they are in the same "time" on your time-line.
I would use the present as the reference point.

Present Value of option I is $8400
(Clearly if you just paid them 8400, it's all done, right?

PV of option II , i = .09/12 = .0075 , n = 48
= 185 ( 1 - 1.0075^-48)/.0075 + 800(1.0075)^-48
= 7434.1846 + 558.8913
= $7993.08

So what do you think?

Answer 2

That is correct.