Answered

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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

Sagot :

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

[tex](1+\frac{5}{100})[/tex]

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

[tex]L\cdot(1+\frac{5}{100})^6[/tex]

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

[tex]L\cdot(1+\frac{5}{100})^6=300[/tex]

Solve for L:

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

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

[tex]223.86[/tex]

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