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Peyton received a graduation gift from his grandparents of $12,700. He does not need the money for the first year of college. So he decided to invest the money in a high interest savings account. If he puts all the money in a high interest savings account paying 8.8% interest compounded semiannually. Suppose that he does not need the money for his sophomore year, so he leaves the money in his account one more year. What will the value of the account be at that time?

Answer :

To calculate the value fo the account, we'll use the compund interest formula:

[tex]V=S(1+I)^n[/tex]

Where:

• V , is the final value of the account

,

• S ,is the amount saved from the begining

,

• I ,is the interest rate

,

• n ,is the number of times the interest is compounded

Now, we know that from graduation to one year after sophomore means a 3 years time frame. If the interest compounds every 6 months (semianually), it means that the interest was compounded 6 times.

Using this with the data given and the formula, we get that:

[tex]\begin{gathered} V=12700(1+\frac{8.8}{100})^6 \\ \rightarrow V=21065.76 \end{gathered}[/tex]

Thereby, the value of the account would be $21,065.76

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