Question

Logan opened a savings account 6 years ago the account earns 5% interest compounded annually. if the current balance is $300.00 how much did he deposit initially

Answer 1

Each year, the initial deposit gets multiplied by a factor of:

`(1+(5)/(100))`

Let L be the initial deposit. 6 years later, the balance of the account will be equal to:

`L\cdot(1+(5)/(100))^6`

On the other hand, the current balance is $300. Therefore:

`L\cdot(1+(5)/(100))^6=300`

Solve for L:

`\begin{gathered} L=(300)/((1+(5)/(100))^6) \\ =(300)/(1.05^6) \\ =223.8646\ldots \\ \cong223.86 \end{gathered}`

Therefore, the initial amount of money in the account 6 years ago, was:

`223.86`