Question

Dahlia is trying to decide which bank she should use for a loan she wants to take out. In either case, 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. Which loan will have the greater total finance charge, and how much greater will it be? Round all dollar values to the nearest cent.

a.
Loan Q’s finance charge will be $83.73 greater than Loan P’s.
b.
Loan Q’s finance charge will be $317.88 greater than Loan P’s.
c.
Loan P’s finance charge will be $20.51 greater than Loan Q’s.
d.
Loan P’s finance charge will be $234.15 greater than Loan Q’s.

I know the answer is not b.

Answer 1

For the answer to the question above, yes you are right that it's not b
The right answer for this is Loan P’s finance charge will be $234.15 greater than Loan Q’s which is the last one among the given choices above.

Answer 2

a. Loan Q’s finance charge will be $83.73 greater than Loan P’s.

Explanation:

To solve this, we will use the formula for loan payment:

`P=((r)/(n)(PV) )/(1-(1+(r)/(n) )^(-nt) )`

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:

`P=((0.058)/(12)(19450) )/(1-(1+(0.058)/(12) )^(-12*9) )`

Solving this we get:

P= $231.59

Dahlia's monthly payment is $231.59. So,her total payment for 9 years will be =
`231.59*9*12=25011.72`

Finance charge will be = total future value minus loan amount plus service charge.

=
`(25011.72-19450)+925` = $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:

`P=((0.055)/(12)(19450) )/(1-(1+(0.055)/(12) )^(-12*10) )`

Solving this we get:

P= $211.08

Dahlia's monthly payment is $231.59. So,her total payment for 10 years will be =
`211.08*10*12=25329.60`

Finance charge will be =
`(25329.60-19450)+690.85=6570.45`

Hence, the total finance charge of bank Q is $6570.45

Now we will find the difference between both bank's finance charges:

`6570.45-6486.72=83.73` dollars

So, we can say that Loan Q’s finance charge will be $83.73 greater than Loan P’s.