Am I doing compound interest wrong?

April 23, 2015 10:07 AM

I'm hoping Metafilter can help me with a stupid math question, but one that's bothering me about how I was taught to compound interest versus some numbers I'm reading/hearing online about a Supreme Court case.

Here's the gist. I got lost in the Wikipedia mindhole this afternoon and ended up at United States v. Sioux Nation of Indians where I saw this:

Finally, under its new authorizing statute, the Claims Court held the Sioux had suffered a taking cognizable under the Fifth Amendment, and were entitled to the value of the land as of the 1877 taking which was $17.1 million, the value of gold prospectors illegally took out of the land computed at $450,000, and 100 years' worth of interest at 5% per year which would be an additional $88 million.[18]

In my head, though, that number seemed...wrong. I was taught annual interest compounded with a formula of B_n = P*(1+i)^n. The balance at year n is the principal times 1+i to the n. So, I plugged into my calculator and I got that 100 years of 5% annual interest on ~$17.5 million is ~$2.3 billion including the principal. The only way I could get to ~$88 million of interest is ~37 years of compounding.

Can someone here help me? This is either an "I don't understand math" or "I can't read the court opinion" answer.

posted by Fortran to Work & Money (5 answers total)

I don't know anything about the decision or the case, but simple interest (non-compound) of 5% per year on $17,550,000 for 100 years is $87,750,000.
posted by The Bellman at 10:12 AM on April 23, 2015

It looks to me as if the interest was not compounded. $17.55 million x 0.05 x 100 = $87.75 million.
posted by brianogilvie at 10:12 AM on April 23, 2015

There is no compounding of the interest in this case.
posted by ssg at 10:12 AM on April 23, 2015

Ahh. Okay. I guess I forgot about ol' simple interest. Thanks!
posted by Fortran at 10:19 AM on April 23, 2015

I dug up the Indian Claims Commission decision, which was later appealed to the Supreme Court (see the bottom of 220-222, or pages 70-72 in the PDF). It explains how the amount was calculated (simple interest). It also cites another case for the 5% interest rate; looking up that decision might tell you where 5% simple interest came from if you want to go down that rabbit hole.

Note that Wikipedia says the money has been earning compound interest post-judgement, as the Sioux refuse to accept the funds and give up their claims for the land.
posted by zachlipton at 10:25 AM on April 23, 2015