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.

Answer 1

Answer:

A is your answer

To solve this, we are going to use the loan payment formula:

where

is the payment

is the present debt

is the interest rate in decimal form

is the number of payments per year

is the time in years

For Bank P

We know from our problem that the the principal of the loan will be $19,450, so . We also know that Bank P offers a nine-year loan with an interest rate of 5.8%, compounded monthly , so  and . Since Dahlia will make monthly payments, and a there are 12 months in a year, . Lets replace the values in our formula:

Now we know that the monthly payment of Dahlia is $231.59. Since we know that she is going to make 12 monthly payments for 9 years, we can calculate the future value of the loan multiplying the amount of the monthly payments ($231.59) by the number of monthly payments (12) by the number of years (9):

Now we know that she is is going to pay $25,011.72 for her loan. Finally, to calculate the total finance charge, we are going to subtract the original loan ( $19,450) from the future value of the loan ($25,011.72), and then, we are going to add the service charge ($925.00):

The total finance charge of bank P is $6,486.72

For Bank Q

We are going to repeat the same procedure as before.

, , , and . Lets replace the values in our formula:

Now that we have our monthly payment, we can calculate the future value of the loan multiplying the amount of the monthly payments ($211.08) by the number of monthly payments (12) by the number of years (10):

Just like before, to calculate the total finance charge, we are going to subtract the original loan ( $19,450) from the future value of the loan ($25,329.6), and then we are going to add the service charge ($690.85):

The total finance charge of bank Q is $6570.45

Notice that the finance charge of ban Q is greater than the finance charge of bank P, so we are going to subtract the finance charge of bank Q from the finance charge of bank P:

We can conclude that Loan Q’s finance charge will be $83.73 greater than Loan P’s. Therefore, the correct answer is a

Step-by-step explanation: