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Why Does APR Rise b/c Payment Due Date Changes?

Question: 
I am using APRWIN 6.2 to calculate the APR for a short-term high-interest installment loan.The payment plan spans up to 20 payments which are 14 days apart with different payment amounts. Although an ideal repayment plan is for about 14*20 = 280 days, I see that the APR changes tremendously based on just the difference between origination date and the first payment due date. First payment period APR 7 919.9443% 14 780% 21 672.4573 I do not understand why the APR rises by 140% just because the first payment due date changes from 14 to 7 days from the origination date. Is this correct? Is there any documentation which explains the formula being used to understand why the APR is highly weighted on the first payment due date instead of the total repayment period?
Answer: 

by Randy Carey:

Are you not adjusting your finance charges for the difference in odd-days? Are you setting your unit periods correctly? You have not provided enough information.

The APR formula is in Appendix J.

Answer: 

by Richard Insley:

The math for APR calculations is not simple but is fully presented here: https://www.bankersonline.com/regulations/12-1026-appj

These are "time value of money" equations. As Randy explains, before calculating the APR, you must determine the payment schedule--accounting for all the dollars that make up each payment. If the interest (and any other part of the Finance Charge) increases when you lengthen the first payment period from 14 to 21 days and decreases when it is shortened to 7 days, these differences must be reflected in the payment schedules for the 3 loans being reviewed. Also, the longer or shorter time period must be reflected in the payment schedule. Based on my best reading of the OP, the "unit period" is 2 weeks (14 days) in all three loans.

Additional thought: Complex issues like this should be handled as a discussion in an open forum--not as a question which can elicit only a one-shot answer. Given additional information, we could arrive at a solution.

First published on 02/11/2018

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