Question

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

Answer 1

Answer:

23 months

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

Step-by-step explanation:

Principal (P) = $2700

rate = 9%

t = ?

Amount = $P(1+\frac{r}{100} )^(t/12)$

Amount = 2700 +500 = $3200

So substituting all our values we get :

$3200 = 2700(1+\frac{9}{100})^(t/12)\\ 3200=2700(1+0.09)^(t/12)\\3200 = 2700(1.09)^(t/12)\\\frac{3200}{2700} =1.09^(t/12)$

So we use log to solve for t :

$t/12=log_{1.09} (\frac{3200}{2700})$

Solving this using a calculator we get:

1.9714966193*12

=23 months