Took out a medical loan but the math doesn't add up

[kms]

My wife had to take out a personal loan in the amount of $44,000 for a major dental procedure. The loan was financed through Proceed Finance and First Security Bank at an APR of 3.99% over two years. These are the numbers on their lending disclosure:

Amount financed: $44,000
Annual Percentage Rate: 3.99%
Total of Payments: $45,847.99
Monthly Rate: $1,910.35

As you can immedlately see, these numbers simply don't add up.

• A loan amount of $44,000 and an APR of 3.99% should have resulted in a monthly rate of $1,910.50 with a total payment amount of $45,852.00 over 24 months
• In order to get to a monthly rate of $1,910.35 the APR would have to be between 3.9821% and 3.9825%
• In order to get to a total payment amount of $45,847.99 the monthly rate would have to be $1,910.33
• At a monthly rate of $1,910.35 the total amount of payments would be $45,848.40

And to make it even more complicated (because simple is for losers!) she also qualified for an immediate 0.25% rate discount by setting up automatic payments. The APR thus immediately decreased to 3.74% yet the monthly rate remained unchanged at $1,910.35 resulting in a interest rate vs. principal shift and a reduced final payment of $1,788.79.


For the first two payments, my calculation returns the following. The total payment is calculated using 3.99% APR, the interest is calculated using 3.74% APR, and the principal is calculated by subtracting the interest at 3.74% from the total at 3.99%:

First month principal: $1,773.37
First month interest: $137.13
Second month principal: $1,778.89
Second month interest: $131.61

The bank's calculution, however, is as follows:

First month principal: $1,773.29
First month interest: $137.06
Second month principal: $1,776.22
Second month interest: $134.13

I realize that the differences are marginal but I'm still confused and would like to find out what went wrong here. Can anyone explain to me where exactly my math went wrong?

[secondcor521]

It's common for banks to make interest and payment calculations using a variety of methods which might create slightly different amounts based on the exact method used.  Some simple examples:

1.  A bank might use a 360 day year and 30 day months even though there are 365 or 366 days in a year and the number of days in a month vary.

2.  The APR may be applied on a monthly, quarterly, semi-annual, annual, or other basis, which would result in different compounding effects.

What is very likely happening is that you're making assumptions about how they're calculating things, and your assumptions are slightly off due to factors similar to the above.

I wouldn't bother tracking down such small differences.  Surely you have other bigger financial fish to fry?

If you really want to resolve the differences, you could either dig into the loan agreement and find out the exact description of their calculations, or you could ask someone at the bank to go through it with you.

[Dicey]

Is the real issue that you're worried about what your wife is going through? If not, perhaps it should be.

[uniwelder]

Has the procedure already happened? If not, you could probably go to a number of excellent facilities around the world (Mexico?) to get it done for less than half the cost. Could you both take off from work long enough?

[Tigerpine]

...
I wouldn't bother tracking down such small differences.  Surely you have other bigger financial fish to fry?

If you really want to resolve the differences, you could either dig into the loan agreement and find out the exact description of their calculations, or you could ask someone at the bank to go through it with you.

I agree with the above.  Their payment terms work in your favor compared to your calculations.  It's probably not worth spending too much time on.

Btw, for a simple amortization of 24 months with monthly payments, the numbers you calculated match those I came up with ($1910.50/mo payment).  Also, out of curiosity, I went to the Proceed Finance website, where they have a calculator to estimate payments.  For a $44k loan with a 2 year repayment plan at 3.99% APR, they come up with a payment of $1910.75 per month.

Which just strengthens my opinion that you shouldn't spend much mental energy on this.  Be happy with the terms you got.

[Metalcat]

Is the real issue that you're worried about what your wife is going through? If not, perhaps it should be.

Sounds like it's probably dental implants based on the price, which isn't fun, but also nothing I would stress too much about if my DH was having it done.

[Metalcat]

Has the procedure already happened? If not, you could probably go to a number of excellent facilities around the world (Mexico?) to get it done for less than half the cost. Could you both take off from work long enough?

Dental care in Mexico is quite good. Dental tourism care in Mexico is frequently horrific and not worth the money you pay for it. Plus good luck getting a local dentist to even touch it once you're back.

[kms]

Thanks, everyone. Yes, I know the differences are small and insignificant in the grand scheme of things. It just bothered me that my math was off and the engineer in me wanted to find out where I went wrong, that's all. @secondcor521's explanation makes perfect sense, thank you.

And yes, she did get All on 4 full dental implants in late December.

[uniwelder]

Has the procedure already happened? If not, you could probably go to a number of excellent facilities around the world (Mexico?) to get it done for less than half the cost. Could you both take off from work long enough?

Dental care in Mexico is quite good. Dental tourism care in Mexico is frequently horrific and not worth the money you pay for it. Plus good luck getting a local dentist to even touch it once you're back.

I guess I’m a bit biased since my wife is from Mexico and knows exactly where to go.

[Metalcat]

Has the procedure already happened? If not, you could probably go to a number of excellent facilities around the world (Mexico?) to get it done for less than half the cost. Could you both take off from work long enough?

Dental care in Mexico is quite good. Dental tourism care in Mexico is frequently horrific and not worth the money you pay for it. Plus good luck getting a local dentist to even touch it once you're back.

I guess I’m a bit biased since my wife is from Mexico and knows exactly where to go.

Yeah. Huge difference between local dental care and Mexican dental tourism. A lot of the dentist who work for those dental tourism clinics have quietly complained about the horrible lack of standards.

I attended a series of lectures from a researcher who specifically researches dental tourism in Mexico.

A family member of mine lived in Mexico for years and married a Mexican woman, but he had to live there for 2 years before the local dental clinic would stop charging him "gringo price" and start charging him the same rate as the locals.

A chunk of my family are from Mexico, so I'm not at all speaking from a bias against Mexican dental care. I'm talking about Mexican dental tourism, which is mostly clinics owned by a tourism company.

Totally different thing.

[secondcor521]

Thanks, everyone. Yes, I know the differences are small and insignificant in the grand scheme of things. It just bothered me that my math was off and the engineer in me wanted to find out where I went wrong, that's all. @secondcor521's explanation makes perfect sense, thank you.

I'm a retired engineer! ;-)