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.

Answer 1

Answer:

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

Step-by-step explanation:

Loan P

Monthly payments for a 9-year 5.8% loan for $19,450 are $231.59, so the total repaid is ...

  108 payments × $231.59 per payment = $25,011.72

Together with the service charge, the cost of the loan is ...

  $25,011.72 + 925.00 - 19,450 = $6,486.72

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Loan Q

Monthly payments for a 10-year 5.5% loan for $19,450 are $211.08, so the total repaid is ...

  120 payments × $211.08 per payment = $25,329.60

Together with the service charge, the cost of the loan is ...

  $25,329.60 +690.85 -19,450 = $6,570.45

__

Difference of charges

The cost of Loan Q exceeds that of Loan P by ...

  $6,570.45 -6486.72 = $83.73 . . . . . matches choice A

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The payment values here were computed using a financial calculator. They can be found using the TVM Solver of a graphing calculator (TI-84), or by any spreadsheet. A number of web sites will also calculate loan payment values, or you can use the formula in your text to compute them yourself.