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.
Answers
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.
Answer:
a. Loan Q’s finance charge will be $83.73 greater than Loan P’s.
Step-by-step explanation:
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Give your answer in its simplest form.
Answers
Answer:
a = √a b = √5 c = √10
ac/b = (√a)(√10)/√5
= √ 10 × a /√5
= √10a / √5
Rationalize the surd
√10a ×√5/(√5)²
= √50a /5
= 5√2a/ 5
= √2a
The final answer is √2a
Hope this helps
Final answer:
You need to substitute the given values into the ac/b equation. After substitization and simplification, the equation ac/b simplifies to √2.
Explanation:
The equation that we need to evaluate is ac/b, using the variables a, b, and c given in the question. So, substituting the given values, we get:
a * c / b = √a * √10 / √5
Since a is equal to √a, we can replace a with √a in the equation, so it then becomes:
√a * √10 / √5 = √(a*10) / √5
Since a is √a, a*10 is therefore √10, so the equation becomes:
√10 / √5
That simplifies to √2 in its simplest form.
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Can someone explain this one?
Answers
The average rate of change in the interval is r{a} = 15.
What is equation modelling? What is a mathematical equation and expression?
- Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
- A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.
- A mathematical equation is used to equate two expressions.
Given is the equation as -
6x −3 = − 5x +7
We have -
6x −3 = − 5x +7
6x + 5x = 7 + 3
11x = 10
x = 10/11
Therefore, thevalue of [x] will be equivalent to 10/11.
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Answers
Answers
Answer:
8.6666666
or
8.7
Step-by-step explanation:
To solve 4x5+6 divided by 3 using BIDMAS, multiply 4 by 5 to get 20, then add 6 to get 26. Finally, divide the sum by 3 to get 8.67.
To solve 4x5+6 divided by 3 using the order of operations known as BIDMAS, we start by performing the multiplication: 4x5=20. Then, we add the result to 6: 20+6=26. Finally, we divide the sum by 3: 26/3= 8.6667 (rounded to 4 decimal places) or 8.67 (rounded to 2 decimal places).
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