# Does interest apply for the last month of an amortization?

I'm working out the loan repayments using the amortization formula

$$\frac{\text{principal} \cdot \text{paymentPercentageInDecimal}}{1 - (1 + \text{paymentPercentageInDecimal})^{-\text{payments}}}$$

I'm confused about the final month. Due to rounding the last month is always a few units below the payment, should the last month's payment be just on the remaining principal or should it have interest applied and be equal to the full amount?

An online calculator (https://www.drcalculator.com/mortgage/ie/) gives (for principal 10000, annual interest 11%, 8 years(monthly interval)

Total interest 5.080.09 Total payments 15,080.09

However the balance for the final month is 155.66 where payment should be 157.08.

My calculations match this calculator except I reduce the payment for the final month to 155.66. Which is correct?

• What is your problem ? Can you say it a bit more clearly ? You pay back 155.66 and pay interest of 1.43. Thus 157.09 has to be paid. – callculus Sep 21 '14 at 19:39
• Thanks for the input. The problem is that I want to know if it is normal to have the final payment be larger and if there is a method to avoid the rounding errors? – LiamRyan Sep 22 '14 at 5:50
• In general it is possible to have a larger or a smaller final payment. The reason is rounding. The more decimal places you use, the greater is the chance, that there will be no difference-but not for sure. But at the most cases, the difference is very very small, like here. – callculus Sep 22 '14 at 10:09