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Suppose that $20,700 is invested in a certificate of deposit for 5 years at 10.5% annual interest to be compounded daily. How much interest will this investment earn?Round your answer to the nearest cent, if necessary. Note: 365 days in a year and 30 days in a month

User Hoo
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Remember that the simple interest formula is:


T=P(1+r)^n

Where:

• T, is the total amount after the investment

,

• P, is the principal

,

• r, is the interest rate

,

• n, is the times the interest was compounded

To get the daily interest, we divide the annual interest rate by 365.


\begin{gathered} r=(10.5)/(100)/365 \\ \\ \rightarrow r=(10.5)/(100\cdot365) \end{gathered}

Since the interest compounds daily for 5 years,


\begin{gathered} n=365\cdot5 \\ \rightarrow n=1825 \end{gathered}

This way, we'll have that:


\begin{gathered} T=20700(1+(10.5)/(100\cdot365))^(1825) \\ \\ \Rightarrow T=34989.86 \end{gathered}

Substracting the principal from this amount, we can get the interest earned:


34989.86-20700=14289.86

We can conclude that the interest earned was $14,289.86

User Ad Infinitum
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