Colleen Ellis bank granted her a single-payment loan of 5000 for 90 days at 9 percent ordinary interest. What is the maturity value of the loan

Remember that the maturity value of a loan is the initial value of the loan plus the interest you have to pay for the loan. To calculate the maturity value of Ellis loan,we are going to use the formula: [tex]A=P(1+rt)[/tex]
where
[tex]A[/tex] the maturity value of the loan 
[tex]P[/tex] is the loan
[tex]r[/tex] is the interest rate in decimal form 
[tex]t[/tex] is the time in years 

Since [tex]t[/tex] is expressed in years, we need to convert 90 days to years. To do that, we are going to divide 90 days by the number of days in a year:
[tex]t= \frac{90}{365} [/tex]
[tex]t= \frac{18}{73} [/tex]
Next, we are going to express the interest rate in decimal form. To do that we are going to divide the rate by 100%:
[tex]r= \frac{9}{100} [/tex]
[tex]r=0.09[/tex]

Now we know that [tex]P=5000[/tex], [tex]r=0.09[/tex], and [tex]t= \frac{18}{73} [/tex]. Lest replace those values in our formula to find the maturity value of Ellis loan:
[tex]A=P(1+rt)[/tex]
[tex]A=5000[1+(0.09)( \frac{18}{73} )][/tex]
[tex]A=5110.96[/tex]

We can conclude that the maturity value of Ellis loan is $5,110.96.