Questions: Goran is taking out a mortgage for 253,000 to buy a new house and is deciding between the offers from two lenders. He wants to know which one would be the better deal over the life of the mortgage loan, and by how much. Answer each part. Do not round intermediate computations, and round your answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) His credit union has offered him a 30-year mortgage loan at an annual interest rate of 5.2%. Find the monthly payment. (b) A bank has offered him a 40-year mortgage loan at an annual interest rate of 3.7%. Find the monthly payment. (c) Suppose Goran pays the monthly payment each month for the full term. Which lender's mortgage loan would have the lowest total amount to pay off, and by how much? Credit union The total amount paid would be less than to the bank. Bank The total amount paid would be less than to the credit union.

Goran is taking out a mortgage for 253,000 to buy a new house and is deciding between the offers from two lenders. He wants to know which one would be the better deal over the life of the mortgage loan, and by how much. Answer each part. Do not round intermediate computations, and round your answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) His credit union has offered him a 30-year mortgage loan at an annual interest rate of 5.2%. Find the monthly payment. (b) A bank has offered him a 40-year mortgage loan at an annual interest rate of 3.7%. Find the monthly payment. (c) Suppose Goran pays the monthly payment each month for the full term. Which lender's mortgage loan would have the lowest total amount to pay off, and by how much? Credit union The total amount paid would be less than to the bank. Bank The total amount paid would be less than to the credit union.
Transcript text: Goran is taking out a mortgage for $\$ 253,000$ to buy a new house and is deciding between the offers from two lenders. He wants to know which one would be the better deal over the life of the mortgage loan, and by how much. Answer each part. Do not round intermediate computations, and round your answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) His credit union has offered him a 30-year mortgage loan at an annual interest rate of $5.2 \%$. Find the monthly payment. $\$$ $\square$ (b) A bank has offered him a 40-year mortgage loan at an annual interest rate of $3.7 \%$. Find the monthly payment. $\$$ (c) Suppose Goran pays the monthly payment each month for the full term. Which lender's mortgage loan would have the lowest total amount to pay off, and by how much? Credit union The total amount paid would be $\$ \square$ less than to the bank. Bank The total amount paid would be $\$ \square$ less than to the credit union.
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate Monthly Payment for Credit Union

Using the formula for monthly mortgage payment, we find the monthly payment for the credit union's 30-year mortgage at an annual interest rate of \(5.2\%\):

\[ M_{cu} = 253000 \cdot \frac{0.0043333(1 + 0.0043333)^{360}}{(1 + 0.0043333)^{360} - 1} \approx 1389.25 \]

Step 2: Calculate Monthly Payment for Bank

Next, we calculate the monthly payment for the bank's 40-year mortgage at an annual interest rate of \(3.7\%\):

\[ M_{bank} = 253000 \cdot \frac{0.0030833(1 + 0.0030833)^{480}}{(1 + 0.0030833)^{480} - 1} \approx 1010.68 \]

Step 3: Calculate Total Payment Over the Life of Each Loan

Now, we compute the total amount paid over the life of each loan:

For the credit union: \[ \text{Total}_{cu} = 1389.25 \cdot 360 \approx 500130.19 \]

For the bank: \[ \text{Total}_{bank} = 1010.68 \cdot 480 \approx 485124.32 \]

Step 4: Determine the Better Deal

To find out which lender offers the better deal, we compare the total payments:

\[ \text{Difference} = 500130.19 - 485124.32 \approx 13005.87 \]

Since \(500130.19 > 485124.32\), the bank offers the better deal.

Final Answer

The credit union's total amount paid would be \(\$13005.87\) more than the bank's total amount paid. Thus, the better deal is from the bank.

\(\boxed{\text{Bank: The total amount paid would be } \$13005.87 \text{ less than to the credit union.}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
At a supermarket, oranges cost 1.30 per pound and pears cost 1.90 per pound. Misha spent less than 10.00 on 2 pounds of oranges and x pounds of pears. Which inequality represents this situation? (1.30+1.90)/2 x<10.00 2(1.30)+1.90 x<10.00 2(1.90)+1.30 x<10.00 2(1.30+1.90) x<10.00
failedAnswered
Which of the following reaction-energy diagrams represents the reaction with the highest equilibrium constant, Keq?
failedAnswered
Question 4 Mark this question One increasingly important success factor and character trait for working in the remote environment of the future is what? Integration with AI Cosmopolitan skills Disruptive business inclinations Ability to work independently SAVE CONTINUE Report an issue with this question
failedAnswered
The formula to calculate the accounting rate of return is: annual income/average investment annual income/initial investment annual income before tax/average investment
failedAnswered
Even Odd Neither