Respuesta :
GIVEN:
We are told that Ryan is taking a short term loan of $2750 for 35 days.
The ordinary interest rate is 4.55%.
Required;
To find the interest he pays
The Loan's maturity value
Step-by-step solution;
To calculate the simple interest on a loan the formula is;
[tex]I=P\times R\times T[/tex]Where the variable T is given in years. However, when the loan is taken for a period less than a year, then the variable T becomes number of days given divided by 360, assuming a 360-day year.
[tex]\begin{gathered} I=interest \\ P=principal(2750) \\ R=annual\text{ }rate(0.0455) \\ T=\frac{35}{360} \end{gathered}[/tex]We can now calculate the interest he pays as follows;
[tex]\begin{gathered} I=2750\times0.0455\times\frac{35}{360} \\ \\ I=12.1649305556 \end{gathered}[/tex]Rounded to the nearest cent, we now have,
[tex]I\approx12.16[/tex]The loan's maturity value is the addition of the principal amount and the amount of interest and that is;
[tex]\begin{gathered} A=P+I \\ \\ A=2750+12.16 \\ \\ A=2762.16 \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} Interest=\text{\$}12.16 \\ \\ Maturity\text{ }value=\text{\$}2762.16 \end{gathered}[/tex]