Given:
[tex]\begin{gathered} \text{ Principal}(p)=\text{\$}1200 \\ \text{ Interest rate}(r)=6\% \end{gathered}[/tex]
The date of borrowed is May 15th and the date of repayment is August 17th.
Required:
We have to find the exact time, interest, and maturity value.
Explanation:
The exact time between 15th May to 17th August is
[tex]t=94\text{ days.}[/tex]
Therefore the time given is
[tex]=\frac{94}{365}\text{ years.}[/tex]
We know that the formula to find the interest is
[tex]\text{ Interest}(I)=\frac{principal\times time\times interest\text{ rate}}{100}[/tex]
[tex]\Rightarrow I=\frac{p\times t\times r}{100}[/tex]
Therefore, the interest is
[tex]\begin{gathered} I=\frac{1200\times\frac{94}{365}\times6}{100} \\ \\ I=\frac{1200\times94\times6}{100\times365} \end{gathered}[/tex][tex]\begin{gathered} =\frac{12\times94\times6}{365} \\ \\ =\text{ \$}18.54 \end{gathered}[/tex]
Therefore, the maturity value is
[tex]\begin{gathered} =1200+18.54 \\ =\text{ \$}1218.54 \end{gathered}[/tex]
Final answer:
Hence the final answer is
[tex]\begin{gathered} \text{ exact time}=94\text{ days} \\ \text{ Interest}=\text{\$}18.54 \\ \text{ Maturity value}=\text{\$}1218.54 \end{gathered}[/tex]
