Andrea, a self-employed individual, wishes to accumulate a retirement fund of $550,000. How much should she deposit each month into her retirement account, which pays interest at a rate of 4.5%/year compounded monthly, to reach her goal upon retirement 45 years from now? (Round your answer to the nearest cent.)

yes

yes yes yes

answer: there are 453.592 grams in a pound.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4