Respuesta :
Loan Q’s finance charge will be $83.73 greater than Loan P’s.
Given
The principal of the loan will be $19,450, and Dahlia will make monthly payments.
Bank P offers a nine-year loan with an interest rate of 5.8%, compounded monthly, and assesses a service charge of $925.00.
Bank Q offers a ten-year loan with an interest rate of 5.5%, compounded monthly, and assesses a service charge of $690.85.
What is a loan payment?
To solve this, we will use the formula for loan payment:
[tex]\rm P=\dfrac{\frac{x}{n}PV}{1-(1+\dfrac{r}{n})^{-nt}}[/tex]
Where 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]\rm P=\dfrac{\frac{x}{n}PV}{1-(1+\dfrac{r}{n})^{-nt}}\\\\P=\dfrac{\frac{0.058}{12}\times 19450}{1-(1+\dfrac{0.058}{12})^{-12 \times 9}}\\\\ P=231.59[/tex]
Dahlia's monthly payment is $231.59. So, her total payment for 9 years will be;
[tex]\rm 231.59\times9\times 12=25011.72[/tex]
A finance charge will be = total future value minus loan amount plus service charge.
= 25011.72 -19450 +925 = $6486.72
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]\rm P=\dfrac{\frac{x}{n}PV}{1-(1+\dfrac{r}{n})^{-nt}}\\\\P=\dfrac{\frac{0.055}{12}\times 19450}{1-(1+\dfrac{0.055}{12})^{-12 \times 10}}\\\\ P=211.08[/tex]
Dahlia's monthly payment is $231.59. So, her total payment for 10 years will be;
[tex]\rm 211.08\times 10\times 12=25329.60[/tex]
The finance charge will be = 25329.60 -19450 +690.85 = $6570.45
Therefore,
The difference between both bank's finance charges:
$6486.72-$6570.45 = $83.73
Hence, Loan Q’s finance charge will be $83.73 greater than Loan P’s.
To know more about loan payment click the link given below.
https://brainly.com/question/8843654
