Answer:
Max APR=6.34%
Explanation:
Present Value of Payments
If someone borrows an amount PV and will make regular payments of R dollars, then the relation between them is
[tex]PV=F_a\cdot R[/tex]
Where
[tex]\displaystyle F_a=\frac{1-(1+i)^{-n}}{i}[/tex]
We know the maximum value for R is $650, thus we can know the minimum value for Fa with:
[tex]\displaystyle F_a=\frac{PV}{R}=\frac{27,500}{650}=42.31[/tex]
It means that we need to find the value of i such that (for n=48):
[tex]\displaystyle \frac{1-(1+i)^{-48}}{i}=42.308[/tex]
This equation cannot be solved in terms of natural or algebraic functions. We need to find the best possible value of i by any numerical approximate method. Let's start off by setting i=0.01
[tex]\displaystyle \frac{1-(1+0.01)^{-48}}{0.01}=37.97[/tex]
It's too far away from the required value. Now we adjust to i=0.005
[tex]\displaystyle \frac{1-(1+0.005)^{-48}}{0.005}=42.58[/tex]
This is a much better value. A final iteration for i=0.00528 gives
[tex]\displaystyle \frac{1-(1+0.00528)^{-48}}{0.00528}=42.302[/tex]
This value is close enough to the required answer. Converting it tho APR:
[tex]i=0.00528\cdot 12\cdot 100=6.34\%[/tex]
