Answer:
Option b - $97.25
Step-by-step explanation:
Given : A $5,000 loan with a 6.25% interest rate compounded monthly spread over 60 months
To find : What would the monthly payment ?
Solution :
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 = $5000
Rate r= 6.25%=0.0625
[tex]i=\frac{0.0625}{12}=0.005208[/tex]
Time = n=60 months
Now, put all the values we get,
[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
[tex]D=\frac{1-(1+0.005208)^{-60}}{0.005208}[/tex]
[tex]D=\frac{1-(1.005208)^{-60}}{0.005208}[/tex]
[tex]D=\frac{1-0.7322}{0.005208}[/tex]
[tex]D=\frac{0.2677}{0.005208}[/tex]
[tex]D=51.415[/tex]
Monthly payment, [tex]M=\frac{A}{D}[/tex]
[tex]M=\frac{5000}{51.415}[/tex]
[tex]M=97.247[/tex]
Approximately The monthly payment is $97.25.
Therefore, Option b is correct.
