8/28/2015 original post -
I recently took out a loan as follows:
- loan amount: $116,000
- interest rate: 4.75%
- term: 360 months
When I calculate the monthly payment it comes out to $605.11/month. This is the answer whether calculating it in Excel using the PMT function, on a Texas Instruments BA II Plus calculator, or by hand plugging all the variables into an equation to calculate the payment. The problem is that the lender shows this loan has a monthly payment of $605.19. The discrepancy may be related to the interest calculation being 30/360 which is specified in the loan document. In the calculations I did, 0.0475/12 was used. But 0.0475/12 is equivalent to 0.0475 * 1/12 which is also equivalent to 0.0475 * 30/360. So, is the lender's monthly payment too high by $0.08 or am I not doing something correctly when calculating the payment?
Note that the equation being used to calculate the payment by hand is as follows:
payment = (interest/12 * loan amount) / (1 - (1 + interest/12)^-term)
11/22/2015 update -
Additional facts pertinent to this problem:
- this is a 5 year balloon mortgage
- funding date was 8/31/2015
- payment due dates are the first day of each month
- day count convention is 30/360
Further figuring -
This loan is for 5 years plus one day. This is because I opted to make loan payments on the 1st of each month instead of the anniversary of the funding date (31st) every month.
Interest due for the additional day the money is borrowed (the 8/31/15 date): $116,000 x 0.0475 ÷ 360 = $15.30555... rounded to dollars and cents: $15.31.
This seems to be the origin of the extra $15+ bucks that Spehro Pefhany identified because when $116,015.31 (from $116,000.00 + $15.31) is plugged into Excel's PMT formula like so:
=-PMT(0.0475/360*30,360,116015.31,0,0) the monthly payment answer exactly matches what's on the loan documents: $605.19.
Because the loan is amortized over 360 months, this math implies that the $15.31 is paid back over 30 years and interest is charged on the $15.31 over that time because it was added to the principal amount when the loan began.
I think the bank's software is incorrectly handling this math; however, the error is in favor of the borrower. The loan statements show that the extra $0.08/payment is being applying to principal rather than interest. Not only does this make the principal of $116,000 decrease slightly faster but it saves the borrower some interest money over the long run because the balance is decreasing at a faster rate. As far as I can tell, the bank does not recover any of the $15.31.
I did notify the banker of these findings as they should be collecting more from the borrower in such a situation ($15.31 in the example above). This example is a small loan but on large commercial loans the bank could be out a significant amount of money.