Question

Mr. Smith invested $2,500 in a savings account that earns 3% interest
compounded annually. He made no additional deposits or withdrawals.
Which expression can be used to determine the number of dollars
in this account at the end of 4 years?

Answer 1

ANSWER: $2731.82
hehehe okay so i'll start off with a list
First you have 2500, then if you compound this after the first year you'll have 0.03*2500+2500
so your list goes like this so far
2500 0.03 (2500)+ 2500
First term Second term
What you begin with What you'll have after the 1st year

Then after the second year you'll have 0.03 more of the second term, 0.03 (2500)+ 2500
So your list now has
2500 0.03 (2500)+2500 0.03[0.03 (2500)+ 2500]+ [0.03 (2500)+2500]
First term Second term Third term
what you after 1st year after 2nd year
begin with

Then after the 3rd year you'll have 0.03 more of the third term, so you have the list
2500, 0.03 (2500)+2500, 0.03[0.03 (2500)+ 2500]+ [0.03 (2500)+2500],
0.03{0.03[0.03 (2500)+ 2500]+ [0.03 (2500)+2500]} +{0.03[0.03 (2500)+ 2500]+ [0.03 (2500)+2500]}

add these up...forget the list i was going to go into the sum of a finite geometric series but you don't have to use that...unless you wanted to find the number of dollars after a large number of years.

Answer 2

(1) 2500(1 0.03)
4
(3) 2500(1 0.04)
3
(2) 2500(1 0.3)
4
(4) 2500(1 0.4)
3