If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?

A) 10,000(x^n)
B) 10,000(x/100)^n
C) 10,000n*(x/100)
D) 10,000(1+x/100)^n
E) 10,000n*(1+x/100)

I chose B, but the official answer is C. Any thoughts?

Let's say n=2 and x=10 percent
$10,000 would earn $1,000 in year 1 and $1,100 in year 2 for a total of $2,100.

Plugging these values into C gives us $2,000.

Simple interest means you get the same interest every year (which is simple, hehe). I think the one you calculated was compounded interest.


Please correct me If I am wrong.


Eric

this is correct. simple interest calculates interest based on the original value of the investment, regardless of the amount of interest that the investment has accrued. therefore, the formula becomes just Prt, where P is the original amount of the investment, r is the interest rate (expressed as a decimal), and t is the time (usually in years).
the actual value of the investment after this time, not to be confused with the above formula (which represents only the total interest), is P + Prt = P(1 + rt).

as the poster above has commented above, you're thinking about compound interest, not simple interest. two totally different animals; don't confuse them.

by the way, it's interesting (heh, "interest"ing) that you didn't apply your number picking to the choice that you picked. if you plug exactly the same numbers into choice (b), you'll get 10,000(0.10)^2, or $100, an absurdly low value. worse yet, according to that formula, the value of the investment would actually shrink every year, and dramatically at that.

even if you didn't realize that you were using the wrong formula, you could still get this problem right by using number plugging: with your n = 2 and x = 10, you get
(a) $10 million (wouldn't that be nice)
(b) $100
(c) $2000
(d) $12,100 (notice that this would be the value of the entire investment after using compound interest, but it's nowhere close to the interest alone)
(e) $22,000
the only one that's even remotely close to your compound-interest estimate is (c), so you should still get the problem correct.
although you get lucky this time; it's extremely common for at least one incorrect answer in a simple-interest problem to come from a compound-interest formula (or vice versa).