Hello Everyone,

I am reviewing a special loan product. The product is a 15 year loan with no payments with a ballon at maturity. The interest rate is 2.49% but the LOS system is calculating an APR of 2.313%.

I verified through the FFIEC APR Calculator and am also coming up with a very similar APR that is lower than the interest rate (2.3108%).

I am scratching my head on this one. How would the APR be less than the interest rate for the term of the loan? If anyone can explain how the math works out on this one, I would appreciate some assistance.

(Insley - if you're checking threads I'd surely appreciate your sage-like wisdom!). Thank you!

Fixed rate loan?

Hi Andy, yes - a fixed rate loan. The closest product I can find are student loans with deferred payments. I've read several articles which state that longer repayment terms and deferred payments may result in an interest rate that is lower than the APR, but none of them explain why?

I unfortunately don't have a PhD in mathematics, so hoping to understand it in layman's terms.

Thank you for the response!

Note - edit for typo

Check section (c)5 of appendix J to Reg Z. I can't give you the why of the math, but the functions are actually pretty easy to follow for single advance single payment transactions.

Thank you Inherent! Appreciate the recommendation. I looked at these examples a little closer. The FFIEC APR Calculator Document Formula gave examples as well. Example iv gives an example of a loan with a two year terms. It appears the calculation is accurate.

I'm just having a hard time wrapping my head around how simple interest accrued annually would result in an APR that is lower than the interest rate. It appears accurate. I just am struggling to understand why.

Hey - at least it's accurate based on Appendix J.

If I understand the particulars of this product, "balloon" actually means "single payment." Are you saying a borrower could walk out of your bank today with a loan proceeds check of $100,000.00 and pay a total of $0.00 until May 11, 2038? Interest is not paid when it accrues? If that is the case, then how much is the single payment, $144,618.01 or $137,350.00?

We will find the answer to your TIL question, but as a once-upon-a-time bank examiner, I wonder what a modern safety & soundness examiner's going to say about a portfolio of loans with no required debt service for such a long term.

Hi Richard!!! Appreciate the response! I'll send you a message! THANK YOU!!

Of course, will post a summary of the outcome so other can find in future searches. Thank you!!

I just wanted to thank Mr. Richard Insley for providing a detailed response that allowed to wrap my head around the APR calculation. I know this took time, and I cannot thank you enough. Appreciate it and definitely owe you a frosty beverage in the future!

We all owe Richard many adult beverages.

Darth & I will post some of the private discussions that got us to a satisfactory answer. Stay tuned...tape at 11.

Here's a summary of Richard's response. It finally makes sense to me now. THANKS RICHARD!

The answer to the quandary is "apples and oranges." Hopefully, the note calls for annual interest (not daily) and it can't be interpreted to mean that interest capitalizes at any time before the date of maturity...because that's what the disclosed Total of Payments represents. This type of interest calculation follows the U.S. Rule--i.e., apples. Since the TOP is the entire payment schedule, the APR calculation must follow Appendix J's instructions for single payment loans--by the actuarial method--oranges.

Using the U.S. Rule to generate the payment schedule (only a single payment in this case) forgoes the opportunity to increase the interest through compounding. Then, the actuarial method in Appendix J assumes that compounding occurred, and the General Equation "uncompounds" the future payment values in order to arrive at the APR (IRR, yield, whatever you want to call the lenders annualized return.) This mismatch in calculation methods (in SP as well as installment loans) always causes the APR to be lower than the simple interest rate that generated the interest in the payment schedule.

Randy - You're in that same category!!! LOL