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
\(M=\frac{\text{Amount}}{\text{Discount factor}}\)
Discount factor \(D=\frac{1-(1+i)^{-n}}{i}\)
Where, Amount = $5000
Rate r= 6.25%=0.0625
\(i=\frac{0.0625}{12}=0.005208\)
Time = n=60 months
Now, put all the values we get,
\(D=\frac{1-(1+i)^{-n}}{i}\)
\(D=\frac{1-(1+0.005208)^{-60}}{0.005208}\)
\(D=\frac{1-(1.005208)^{-60}}{0.005208}\)
\(D=\frac{1-0.7322}{0.005208}\)
\(D=\frac{0.2677}{0.005208}\)
\(D=51.415\)
Monthly payment, \(M=\frac{A}{D}\)
\(M=\frac{5000}{51.415}\)
\(M=97.247\)
Approximately The monthly payment is $97.25.
Therefore, Option b is correct.
