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Sagot :
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:
[tex]A(n)=P\left(1+\frac{r}{k}\right)^{nk}[/tex]Using the compound period formula, we first, calculate the amount in her account at the end of 1 year.
[tex]\begin{gathered} A(1)=8000\left(1+\frac{0.05}{12}\right)^{12\times1} \\ A(1)=\$8409.30 \end{gathered}[/tex]This means that the interest she made during the first year is:
[tex]\text{ Interest during the first year}=8409.30-8000=\$409.30[/tex]Next, calculate the amount in her account at the end of the second year.
[tex]\begin{gathered} A(2)=8000\left(1+\frac{0.05}{12}\right)^{12\times2} \\ A(2)=\$8839.53 \end{gathered}[/tex]Since she paid back all the interest she made during the first year, the amount Diana was left with is:
[tex]\begin{gathered} 8839.53-409.30 \\ =8,430.23 \end{gathered}[/tex]Diana was left with $8,430.23.
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