Nathan opens a new savings account and makes an initial deposit of $400.

if the account earns 2% annual interest, how much interest will he earn in 9 months?

$6

Step-by-step explanation:

To find how much Nathan will get in 9 months, we use the formula:

Let's break down the variables that we have.

I = ?

P = 400

r = 2% or 0.02

t = 9/12 or 0.75

The time is 0.75, because the interest is applied annually.

Now let's plug in our values to the formula.

Nathan will earn $6 in interest in 9 months.

the graph on the bottom right

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