Answer:
The amount of Mark's Total payment is $7256.91.
Step-by-step explanation:
Given : Mark borrowed $5,500 at 11.5 percent for five years.
To find : What is the amount of Mark's total payment?
Solution :
First we find the monthly payment,
Formula of monthly payment
[tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Where, Amount = $5500
Rate r= 11.5%=0.115
[tex]i=\frac{0.115}{12}=0.00958[/tex]
Time = 5 years
[tex]n=5\times12=60[/tex]
Now, put all the values we get,
[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
[tex]D=\frac{1-(1+0.00958)^{-60}}{0.00958}[/tex]
[tex]D=\frac{1-(1.00958)^{-60}}{0.00958}[/tex]
[tex]D=\frac{1-0.5643}{0.00958}[/tex]
[tex]D=\frac{0.4357}{0.00958}[/tex]
[tex]D=45.4739[/tex]
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
[tex]M=\frac{5500}{45.4739}[/tex]
[tex]M=120.948[/tex]
Monthly payment is $120.948
The amount is [tex]120.948\times 60=7256.91[/tex]
Therefore, The amount of Mark's Total payment is $7256.91.
