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:
