Recently, I received yet another promotion from yet another company offering me money at zero percent interest with the predictable asterisk next to the zero percent. Instead of just shredding the offer I decided to create a downloadable Excel template to analyze the offer, which was an interest-free 18 month loan for a 4% transaction fee with a minimum $10 fee.

Obviously, the transaction fee makes sure that the money is not ‘free.’ So, how does one calculate the cost of the loan? I settled on an “effective interest rate.”

For a version in a page by itself (i.e., not in a scrollable iframe as below) visit http://www.tushar-mehta.com/publish_train/xl_vba_cases/0920%20free%20money.shtml

Interestingly I ran several variations of the calculation y=100*(((1000/960)^X)-1)

and the given result was beneath the lowest here.

Y..............X

360/(365+180)..2.73

12/18..........2.76

(360/(360+180).is identical)

365/(365+180)..2.77

365/(360+180)..2.80

This illustrates potential 360 vs. 365 biases, and 30 day month approximation effects in fractional (e.g. nonannual) interest calculations.

BTW 2.76 (using 12/18) was obvious to me without blinking. Even with a strict 30 day month assumption, 360/540 is also 2.76. My next guess of what Excel might have used would have been 365/540, and then 365/545.

As to how 2.72 was reached, Tushar used an actual day count to calculate a true effective daily rate and multiplied by 365. Many mathematicians would argue to use ^365 rather than *365. Yet multiplication is somewhat consistent with U.S. consumer "APR," although it is not actually the "effective annual interest rate" (some mathematicians shun the APR approach)

`Finally, if you want to use 183, the actual days between April and October (which Tushar used), the results above change, though none exactly replicate the "*365" result of 2.7191%`