TVM Amortization Rounds to Cents (or other)

[Rick314]

I've used HP Time Value of Money (TVM) calculators and programs for decades and just realized that my HP 10bII+ (and likely other HP calculators), when doing Amortization math, round BAL and PMT and INT to the current display resolution before doing the math. This is very useful, documented in the manual appendix that shows equation details, and has interesting impact.

For example, from the HP 10bII+ User Guide p76: P/YR = 12; N = 360; I/YR = 7.75; PV = 180,000; FV = 0; End Mode finds PMT = -1,289.54. So far so good. But now find amortization results for the last payment (#360) with display resolution set to 2 (cents, the typical default) versus 9 (or any high resolution). With high resolution you end up with a BALance of $0.00 as expected. But with cents display, you end up with a BALance of $3.00, which is correct if you made actual monthly payments to cents resolution for 30 years. I made an Excel spreadsheet with 360 rows to prove to myself this is what is going on.

There is a related defect in the HP 10bII+ User Guide p76 example. The manual shows PRINciple paid after the first 12 payments as "-1,579.84". If the calculator display resolution is the default cents (as implied by the ".84" in the answer) the calculator value is -1,579.82. The .84 value is the full-resolution value, likely found by the User Guide author using higher display resolution and then manually rounding to cents resolution. Doing this User Guide example and seeing the $0.02 difference is what prompted me to look into these details. Just my two cents. (:-)

[Dave Britten]

Some of the other financial calculators I've used don't automatically round PMT, but I think most round the interest and principal when amortizing a single payment. Can't remember what the 12C does, but the 17BII manual says it rounds PMT automatically. According to the manual, it rounds PMT, calculates interest as BAL*i rounded to the current display mode, and subtracts that from PMT to arrive at the principal amount.

[Albert Chan]

(04-03-2021 08:44 PM)Rick314 Wrote:  But with cents display, you end up with a BALance of $3.00, which is correct if you made actual monthly payments to cents resolution for 30 years. I made an Excel spreadsheet with 360 rows to prove to myself this is what is going on.

Yes. I tried calculated it (in cents, so to avoid binary/decimal conversion errors)
I used rint(), i.e. bankers rounding.

lua> n=360; r=7.75/1200; pv=18e6; pmt=-128954 -- whole cents
lua> k = (1+r)^n -- compounding factor
lua> rint(pv*k + pmt*(k-1)/r) -- calculated balance, in cents
289

Now, actually round the balance, for each period

lua> for i=1,n do pv = pv + rint(pv*r) + pmt end
lua> pv -- actual balance, in cents
300