Answer:
a. Loan Q’s finance charge will be $83.73 greater than Loan P’s.
Step-by-step explanation:
To solve this, we will use the formula for loan payment:
[tex]P=\frac{\frac{r}{n}(PV) }{1-(1+\frac{r}{n} )^{-nt} }[/tex]
Here,
P is the payment ; PV is the present debt; r is the interest rate; n is the number of payments per year; t is the time
Working for bank P:
PV = 19450
r = 5.8 or 0.058
t = 9
n = 12
Putting the values in the formula we get:
[tex]P=\frac{\frac{0.058}{12}(19450) }{1-(1+\frac{0.058}{12} )^{-12*9} }[/tex]
Solving this we get:
P= $231.59
Dahlia's monthly payment is $231.59. So,her total payment for 9 years will be = [tex]231.59\times9\times12=25011.72[/tex]
Finance charge will be = total future value minus loan amount plus service charge.
= [tex](25011.72-19450)+925[/tex] = $6486.72
Hence, the total finance charge of bank P is $6,486.72
Working for bank Q:
PV = 19450
r = 5.5 or 0.055
t = 10
n = 12
Putting the values in the formula we get:
[tex]P=\frac{\frac{0.055}{12}(19450) }{1-(1+\frac{0.055}{12} )^{-12*10} }[/tex]
Solving this we get:
P= $211.08
Dahlia's monthly payment is $231.59. So,her total payment for 10 years will be = [tex]211.08\times10\times12=25329.60[/tex]
Finance charge will be = [tex](25329.60-19450)+690.85=6570.45[/tex]
Hence, the total finance charge of bank Q is $6570.45
Now we will find the difference between both bank's finance charges:
[tex]6570.45-6486.72=83.73[/tex] dollars
So, we can say that Loan Q’s finance charge will be $83.73 greater than Loan P’s.
