Question

How long does it take a 2700 dollar investment compounded monthly at 9% to make 500 dollars

Answer 1

23 months

Also please note that it's everytime ^t/12 not (^t)/12

Explanation:

Principal (P) = $2700

rate = 9%

t = ?

Amount =
`P(1+(r)/(100) )^(t/12)`

Amount = 2700 +500 = $3200

So substituting all our values we get :

`3200 = 2700(1+(9)/(100))^(t/12)\\ 3200=2700(1+0.09)^(t/12)\\3200 = 2700(1.09)^(t/12)\\(3200)/(2700)  =1.09^(t/12)`

So we use log to solve for t :

`t/12=log_(1.09) ((3200)/(2700))\\`

Solving this using a calculator we get:

1.9714966193*12

=23 months