A savings account is started with an initial deposit of $700. The account earns 1.5% interest compounded annually. Write an equation to represent the amount of money in the account as a function of time in years. Then find the amount of time it takes for the account balance to reach $1,200. Show your work.

It will take 36.2 years.

Step-by-step explanation:

The principal amount is $700. This principal amount earns 1.5% interest that is compounded annually.

Therefore, from the formula of compound interest, we can write

, where S is the maturity sum and P is the principal invested and r% is the interest which is compounded annually and t is the number of years.

So, in our case, the equation will be

............ (1) (Answer)

Now, if the maturity sum, S = $1200, then,

⇒

Now, taking log both sides,

t(log 1.015) = log 1.714

⇒ t = 36.2 years.