Answer:
[tex]R=\$145.12[/tex]
Step-by-step explanation:
Compound Interest
This is a well-know problem were we want to calculate the regular payment R needed to pay a principal P in n periods with a known rate of interest i.
The present value PV or the principal can be calculated with
[tex]P=F_a\cdot R[/tex]
Solving for R
[tex]\displaystyle R=\frac{P}{F_a}[/tex]
Where Fa is computed by
[tex]\displaystyle F_a=\frac{1-(1+i)^{-n}}{i}[/tex]
We'll use the provided values but we need to convert them first to monthly payments
[tex]i=7\%=7/(12\cdot 100)=0.00583[/tex]
[tex]n=3*12=36[/tex]
[tex]\displaystyle F_a=\frac{1-(1+0.00583)^{-36}}{0.00583}[/tex]
[tex]F_a=32.386[/tex]
Thus, each payment is
[tex]\displaystyle R=\frac{4,700}{32.386}=145.12[/tex]
[tex]\boxed{R=\$145.12}[/tex]
