Question

Suppose you invest $500 in a savings account that pays 3.5% annual interest. When will the account contain at least $650?

Answer 1

@amistre64

Answer 2

I have the equation \(A(t)=a(1+2)^t\) that I believe I need to use.

Answer 3

oops, that 2 should be r

Answer 4

so I think a is 500 and r would be 0.035... and I think I'm solving for t...

Answer 5

what is a in the question
what is r ?

Answer 6

:-) yep right

Answer 7

a is the initial amount and r is the rate of growth, or the rate of decay

Answer 8

and A would be 650?

Answer 9

okay there is two ways you can solve this problem
first one you can replace t by 2 3 or 5 6 and see which one give at least 650 when you solve right side
another way
replace a(t) by 650

Answer 10

so do I need to make a table?

Answer 11

nope for example first method
i'll replace a by 500 and r by .035 and try 2 for t \[a(t)= 500(1+.035)^2\]
like this now i will solve right side
if i get at least 650 then 2 is my answer

Answer 12

so it's a guess and check thing? would a table work?

Answer 13

and 2 doesn't work.

Answer 14

yep but i guess you should do by 2nd method :) \[\huge\rm 650 = 500(1+.035)^t\]

Answer 15

yep guessing for first one :)

Answer 16

yep but i guess you should do by 2nd method :) \[\huge\rm 650 = 500(1+.035)^t\]
do you know how to solve this one ?

Answer 17

is there a way to solve it algebraically to find t?

Answer 18

do you know how to take ln ?? log ?

Answer 19

No, that's next. This came first...

Answer 20

okay then guess :)

Answer 21

The only way I know how to do this is to make a table... :/

Answer 22

okay.

Answer 23

yep that one :-)

Answer 24

I get 8.. because it equals 658.4045...

Answer 25

so after 8 years.

Answer 26

:-)

Answer 27

Can you help with some more?

Answer 28

i'll try :)