If you deposit $6000 into an account paying 6% annual interest compounded monthly, how long until there is $8000 in the account?

It will take 4.4 years to gain $8000.

Step-by-step explanation:

Substitute the values in the formula.  

A = P (1+r/n) nt                    8000 = 6000 (1+0.06/12) 12t  

Use BEDMAS (order of operations) and solve the value in the brackets.

8000 = 6000 (1.005) 12t

Divide both sides by 6000  

1.3 = (1.005) 12t

Take the logarithm of both sides.  

log (1.3) = log (1.005) 12t

Include the exponent in the equation.

log (1.3) = (12t) (log 1.005)  

Divide both sides by log 1.005.

(log⁡(1.3))/(log⁡(1.005)) = 12t

Find out the log.  

52.6039 = 12t  

Divide both sides by 12.  

4.4 = t  

I'm attaching a word document where everything is organized.

Step-by-step explanation:

Distributive property: ⇒

First you had to add 57 from both sides of an equation form.

Hope this helps!

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-Charlie