On Tue, 10 Apr 2007 14:04:58 -0400, "Stephen J. Herschkorn" <email@example.com> wrote:
>firstname.lastname@example.org wrote: > >>I ran across old (1926) SAT math problems and >>one of them puzzles me -- it's stated as follows: >> >> A man buys a house and lot for $8,500 but is obliged to pay >> $500 back taxes on the property. He leases the property at the >> rate of $75 a month. What rate of interest does this investment >> bear? >> >>I think I'm missing something here -- any clue? >> > >My guess is that they want the nominal annual rate of interest for the >following infinite stream of cash flows: A cost of $9000 at month zero >and an income of $75 every month thereafter. The monthly rate could be >figured out as 75 / 9000, yielding a nominal rate of 16.7% per annum.
Except that's the wrong answer.
An income of $75 per month equates to $900 per year, so the simple annual interest rate is 10%, not 16.7%.
>As to what they wanted exactly, perhaps in 1926 the standard terminology >was more well-known to the average college-bound student. Or, if >test-takers got to write out the answer (as opposed to choosing a >lettered answer), they could make precise what they are giving.
Since the test being discussed was an SAT test, it's almost certain that it was multiple choice. I'll guess that the choices were something like the following:
(a) 10% [correct answer]
(b) 10.58% [failed to add the tax, answer rounded to nearest hundredth]
(c) (11 and 1/4)% [subtracted the tax instead of adding]
(d) (8 and 1/3)% [forgot to multiply $75 by 12, and also, moved the decimal point one place too far to the right]
This is not a sophisticated problem -- we're talking about the SAT. Thus, the test takers can be presumed to be a very general audience of high school students. The test could legitimately assume math knowledge up to what's now called precalculus, but most problems would be below that level, requiring just basic reasoning skills and limited math.