Hi, there. I'm happy to help with this.
Let r be the interest rate, expressed as a decimal (i.e. 5% = 0.05).
Simple interest will increase to
1200 + 1200r + 1200r = 1200*(1 + 2r)
Compound interest will increase to
1200(1 + r)(1 + r) = 1200*(1 + 2r + r^2)
It makes sense that the only term that's different between the two expressions is the r^2 term, which is
interest on interest. That, right there, is the big idea of compound interest. In simple interest, you get interest only on the principle. In compound interest, you get interest on the principle
and on the previous interest.
1200*(r^2) = 132
Divide both sides by 12
100*(r^2) = 11
r^2 = 11/100 = 0.11
I get r = 0.331662479, which is not an answer choice. Something is funky here.
If the difference between two-years simple vs. two-years compound were
$12, not $132, then the answer would be r = 10%, choice A.
If the difference between
one year of interest vs. two-years compound interest were $132, then again, the answer would be r = 10%, choice A.
I think something got confused here about what is being asked, either a problem at the source or a problem in miscopying at some point along the way.
Does the approach I used make sense? Do you have any questions?
Mike
