You put $500 in an account that earns 4% annual interest. the interest earned each year is added to the principal to create a new principal. find the total amount in your account after each year for 3 years.
a) year 1 = $
b) year 2 = $
c) year 3 = $

A) $ 520

B) $ 540.8

C) $ 562.432

Step-by-step explanation:

Since, the amount formula in compound interest calculated annually,

Where,

P = principal amount,

r = annual interest rate,

t = number of years,

A) P = $ 500, r = 4% = 0.04, t = 1,

B) P = $ 520, r = 0.04, t = 1,

C) P = $ 540.8, r = 0.04, t = 1,

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