Time Value of Money Question For the following Question



The Answer is 


First:
Scenario 1 : I wonder how the customer pay as whole 12000 dollar after 12 years for a 8525 dollar product if the interest rate = 0%

I think that , there is about 3% interest 

Second:
What is the criteria upon which the company decide in first scenario to pay 1000$ /year and for the second scenario to pay the full amount?
This is a very poorly written question. 

The gist of the question is this: should a company take a lump-sum payment from a customer of \$8,525 or a \$12k payment that is spread uniformly over 12 years. The thing the question wants you to consider between 1a and 1b is that in 1a the company cannot earn interest (which the answer just assumes is compounding) and in 1b the company can earn 7% interest. 



For the given answer, part 1a is saying that, since the company cannot earn interest on investments, it is better to just take the \$12k. However, one ought to know something about how this company discounts to actually answer this question. That is, one should make this comparison by comparing \$8,525 to the discounted present value of the \$12k, taking into account that the \$12k is received in payments spread uniformly over 12 years. The real answer to this question as written is, ' IT DEPENDS'.

Part 1b is saying that $8,525(1+.07)^{12} \equiv 19,199.93 &gt; 12,000$ and so the company should take the lump-sum payment and invest it. HOWEVER, this is again the wrong way to answer this question. Instead, one should compare 
$8,525(1+.07)^{12}$ with the money the firm will have if it chooses the \$12k and subsequently invests each annual payment. This value is \$19,140.64 (link to calculate). The answer here is correct but for the wrong reason. 



Really, this is a very bad question and a very bad answer.