Question

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.

Answer 1

`S = 700(1.015)^(t)`

It will take 36.2 years.

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

`S = P(1 + (r)/(100) )^(t)`, 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

`S = 700(1 + (1.5)/(100))^(t) = 700(1.015)^(t)` ............ (1) (Answer)

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

`1200 = 700(1.015)^(t)`

⇒
`(1.015)^(t) = 1.714`

Now, taking log both sides,

t(log 1.015) = log 1.714

⇒ t = 36.2 years.