"Real" total cost of zero-interest loan

Question

Many solar panel manufacturers and banks are offering zero-interest loans to induce buyers to pull the trigger on a residential install. I have been doing some calculations and it seems that if I get a competitive quote then it should be rational for me to buy some panels (in a purely economic sense-not counting the value of making a statement). However, I do not know how to think clearly about the real cost of a zero-interest loan. If the loan is for $P$, and the inflation rate is $r$ with a term of $y$ years divided into $n$ payments, what is the "real" cost of the loan?

Answer 1

Note that the "real cost" in this case is less than the cost of the panels, since you will be paying back the loan with inflated dollars. The actual value depends on the frequency of payment. If it's all at once at the end of $y$ years you'll have to pay $P$ dollars then, but that will be just $P/(1+r)^y$ 2017 dollars.

For yearly installments the calculation is straightforward but a little tedious. The bill in year $k$ will be $$ \frac{P/y}{(1+r)^k} $$ so that the total cost is given by $$ P\left[\frac{1 - (1+r)^{-y}}{ry} \right] $$ Assuming 2% inflation and a 10 year repayment, this means your total cost is ${\sim}0.89P$.

For $n$ payments when $n > y$ you have to pay attention to the partial inflation during each year. I'm sure you can't estimate $r$ well enough over $y$ years to make that computation precise enough to be worth the effort.