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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.

Respuesta :

Answer:

[tex]S = 700(1.015)^{t}[/tex]

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

[tex]S = P(1 + \frac{r}{100} )^{t}[/tex], 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

[tex]S = 700(1 + \frac{1.5}{100})^{t} = 700(1.015)^{t}[/tex] ............ (1) (Answer)

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

[tex]1200 = 700(1.015)^{t}[/tex]

⇒ [tex](1.015)^{t} = 1.714[/tex]

Now, taking log both sides,

t(log 1.015) = log 1.714

⇒ t = 36.2 years.

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