Question

Help With One Question!! Please do "NOT" tell me the answer Thank Youu!
You deposit $2,500 in an account that pays 5.7% interest compounded annually.
What is the balance after five years?

Answer 1

do you know the formula?

Answer 2

at the end of each year you take the interest collected on the interest and add it back into the account.

\[a_n=I\ a_{n-1}+a_{n-1}\]

Answer 3

the interest collected on the account ...

Answer 4

to increase a number by 5.7% is to increase it by 0.057
if you call the number \(P\) then to increase it by 0.057 means you will have
\[P+.057P\] which, by the distributive property is the same as \(P(1.057)\)

Answer 5

if you increase it by .057 twice, that is the same as \(P(1.057)\times (1.057)=P(1.057)^2\)

Answer 6

now you want to increase it by .057 5 times, so you should be good to go right?

Answer 7

i multiplied .057 5 times and i got a huge number

Answer 8

what is $2,500*.057 equal ?

Answer 9

yr1: 2500 * .057 added back to 2500
balance = (2500*.057 + 2500)

yr2: (2500*.057 + 2500)*.057 added back to (2500*.057 + 2500)
balance = (2500*.057 + 2500)*.057 + (2500*.057 + 2500)

this is the basic workings of it, and we can simplify the process if we want to

Answer 10

Thanks I got It now :)

Answer 11

yep, good luck :)