You'd think a CPA would know better

Buckethead Buckethead

Speaking of loan repayment calculators, certain acquaintances of mine are dealing with a client who wants an application that calculates loan payments. This client is a CPA in charge of finances for a large entity. This individual believes that a loan repayment schedule should look like this:

For a loan of 1000, for ten years, at 5% APR, with yearly payments.

Payment Due Date Payment Amount Principal Interest Cumulative Principle Cumulative Interest Principle Balance
8/1/05 150.00 100.00 50.00 100.00 50.00 900.00
8/1/06 150.00 100.00 50.00 200.00 100.00 800.00
8/1/07 150.00 100.00 50.00 300.00 150.00 700.00
8/1/08 150.00 100.00 50.00 400.00 200.00 600.00
8/1/09 150.00 100.00 50.00 500.00 250.00 500.00
8/1/10 150.00 100.00 50.00 600.00 300.00 400.00
8/1/11 150.00 100.00 50.00 700.00 350.00 300.00
8/1/12 150.00 100.00 50.00 800.00 400.00 200.00
8/1/13 150.00 100.00 50.00 900.00 450.00 100.00
8/1/14 150.00 100.00 50.00 1000.00 500.00 0.00

Plugging the loan amount, number of payments and interest into a standard loan calculator, you get something like this:

Payment Due Date Payment Amount Principal Interest Cumulative Principle Cumulative Interest Principle Balance
8/1/05 129.50 79.50 50.00 79.50 50.00 920.50
8/1/06 129.50 83.48 46.02 162.98 96.02 837.02
8/1/07 129.50 87.65 41.85 250.64 137.88 749.36
8/1/08 129.50 92.04 37.47 342.67 175.34 657.33
8/1/09 129.50 96.64 32.87 439.31 208.21 560.69
8/1/10 129.50 101.47 28.03 540.78 236.24 459.22
8/1/11 129.50 106.54 22.96 647.33 259.21 325.67
8/1/12 129.50 111.87 17.63 759.20 276.84 240.80
8/1/13 129.50 117.46 12.04 876.66 288.88 123.34
8/1/14 129.50 123.34 6.17 1000.00 295.05 0.00

Given that the stated purpose of using the first formula was to save the loan recipient money, the client's stubborn refusal to admit that maybe their conception of simple interest loan repayment plans is a bit out of touch with standard accounting practice, general wisdom and in fact reality.

A few things to consider: while the second scheme is not exactly intuitive, the total interest paid makes sense when you consider that over the term of the loan, you will owe half of the loan amount, on average. The decreasing interest/increasing principal as percentages of the payment amount make sense when you realise that at any given moment, you're paying 5% interest on the remaining balance. It has to work that way if you want a constant payment over the term of the loan.

I am not an accountant. I have software do my taxes, and I haven't ever thought about this subject in any depth whatsoever until today. But what is obvious to me is not to the client, who in the interest of protecting his loan recipients is proposing terms that a loan shark would love - especially the 50% interest on the last payment.

Posted by Buckethead Buckethead on   |   § 2

§ 2 Comments

2

I did 8 years at a CPA firm for my first "grown up job" (though not as an accountant), and I can tell you that they were good business folk, good at accounting, and largely utterly innumerate with anything that wasn't addition, subtraction, multiplication, or division.

A question about Euler's number might get a response "You mean the Houston Oilers?". Our tax partner had a Masters in Math, but aside from she and me, a mathematical (as opposed to simple arithmetic) clue was hard to find.

And yet, the example you provide above STILL takes the freakin' cake - Excel can do that calc automatically, for Gaia's sake!

Patton Patton

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