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42 votes
42 votes
Diana put $8000 in a 10-year CDpaying 5% interest compoundedmonthly. After 2 years, shewithdrew all her money, and as anearly withdrawal penalty, she paidback all the interest she madeduring the first year. How muchmoney was Diana left with?

User Gertie
by
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1 Answer

26 votes
26 votes

Answer:

$8,430.23

Explanation:

From the statement of the problem:

• The principal amount = $8,000

,

• Interest Rate = 5%

,

• Compounding Period = 12 (Monthly)

The compound interest formula is given as:


A(n)=P\left(1+(r)/(k)\right)^(nk)

Using the compound period formula, we first, calculate the amount in her account at the end of 1 year.


\begin{gathered} A(1)=8000\left(1+(0.05)/(12)\right)^(12*1) \\ A(1)=\$8409.30 \end{gathered}

This means that the interest she made during the first year is:


\text{ Interest during the first year}=8409.30-8000=\$409.30

Next, calculate the amount in her account at the end of the second year.


\begin{gathered} A(2)=8000\left(1+(0.05)/(12)\right)^(12*2) \\ A(2)=\$8839.53 \end{gathered}

Since she paid back all the interest she made during the first year, the amount Diana was left with is:


\begin{gathered} 8839.53-409.30 \\ =8,430.23 \end{gathered}

Diana was left with $8,430.23.

User Oliverguenther
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