Answer:
Option 3 or b - The monthly payment is $235.13.
Step-by-step explanation:
Given : A 6 year loan of $15,250 at 3.5% compounded monthly.
To find : Monthly payment ?
Solution :
The formula to find monthly payment is
[tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor is [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Substitute in the formula,
[tex]M=\frac{A}{\frac{1-(1+i)^{-n}}{i}}[/tex]
[tex]M=\frac{A\times i}{1-(1+i)^{-n}}[/tex]
where, A is the amount A=$15250
r is the rate = 3.5%=0.035 compounded monthly
[tex]i=\frac{r}{12}=\farc{0.035}{12}=0.00291[/tex]
time t=6 years
Time in months [tex]n=t\times 12=6\times 12=72[/tex]
Substitute all the values in the formula,
[tex]M=\frac{15250\times 0.00291}{1-(1+0.00291)^{-72}}[/tex]
[tex]M=\frac{44.479}{1-(1.00291)^{-72}}[/tex]
[tex]M=\frac{44.479}{1-0.8112}[/tex]
[tex]M=\frac{44.479}{0.18916}[/tex]
[tex]M=235.13[/tex]
Therefore, The monthly payment is $235.13.
So, Option 3 or b is correct.
