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Part 1

Use 

StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt Baseline right bracket EndEndFractionPrn1−1+rn−nt 

to determine the regular payment​ amount, rounded to the nearest dollar. Consider the following pair of mortgage loan options for a 

​$155 comma 000155,000 

mortgage. Which mortgage loan has the larger total cost​ (closing costs​ + the amount paid for points​ + total cost of​ interest)? By how​ much?

Mortgage​ A: 

3030​-year 

fixed at 

6.256.25​% 

with closing costs of 

​$29002900 

and 1 point.

Mortgage​ B: 

3030​-year 

fixed at 

4.54.5​% 

with closing costs of 

​$29002900 

and 

22 

points.

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Part 1

Choose the correct answer​ below, and fill in the answer box to complete your choice.

​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)

A.

Mortgage B has a larger total cost than mortgage A by 

​$enter your response here.

B.

Mortgage A has a larger total cost than mortgage B by 

​$enter your response here.

To determine which mortgage has the larger total cost, we need to calculate the monthly payments for both mortgages and then add up the closing costs, the amount paid for points, and the total interest paid over the life of each loan.

### Step 1: Calculate Monthly Payment for Each Mortgage
The formula for the monthly payment $ M $ is given by:

\[
M = \frac{P \times \left(\frac{r}{n}\right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]

Where:
- $ P $ is the loan principal (here $155,000)
- $ r $ is the annual interest rate (in decimal form)
- $ n $ is the number of payments per year (typically 12 for monthly payments)
- $ t $ is the loan term in years (here 30)
- $ nt $ is the total number of payments over the life of the loan

#### Mortgage A:
- Principal: $ P = 155,000 $
- Annual interest rate: $ r = 6.25\% = 0.0625 $
- Loan term: 30 years
- $ n = 12 $

#### Mortgage B:
- Principal: $ P = 155,000 $
- Annual interest rate: $ r = 4.5\% = 0.045 $
- Loan term: 30 years
- $ n = 12 $

### Step 2: Calculate Points and Closing Costs

Points are calculated as a percentage of the loan amount. For each point:
- 1 point = 1% of the loan amount.

#### Mortgage A:
- 1 point = 1% of $155,000 = $1,550.
- Closing costs = $2,900.

#### Mortgage B:
- 2 points = 2% of $155,000 = $3,100.
- Closing costs = $2,900.

### Step 3: Calculate Total Interest Paid Over the Loan Term

Once we calculate the monthly payments, the total amount paid over the life of the loan is the monthly payment multiplied by the total number of payments (which is 12 payments per year for 30 years, or 360 total payments).

The total interest paid is the total amount paid over the life of the loan minus the original loan principal.

### Step 4: Compare Total Costs

After calculating the total interest for both mortgages, add the points and closing costs to compare the total cost of each mortgage.

I'll calculate the monthly payments for both mortgages and then compare the total costs.The total cost for each mortgage, including interest, points, and closing costs, is as follows:

- **Mortgage A**: $193,020
- **Mortgage B**: $133,730

The difference between the two mortgages is approximately **$59,290**.

Thus, **Mortgage A** has a larger total cost than Mortgage B by about **$59,290**.

Would you like further details or clarification?

### Related Questions:
1. What is the exact calculation of total interest paid for each mortgage?
2. How do the points affect the overall cost of the mortgage?
3. What are the advantages of paying points upfront in a mortgage?
4. How would the total cost change if the mortgage terms were reduced to 15 years?
5. What is the impact of a higher closing cost on the total mortgage cost?

**Tip:** Refinancing to a lower interest rate may save substantial money in the long term if you plan to stay in the house for a long period.

Use the formula to determine the regular payment amount, rounded to the nearest dollar. Consider the following pair of mortgage loan options for a $155,000 mortgage. Which mortgage loan has the larger total cost (closing costs + the amount paid for points + total cost of interest)? By how much? Mortgage A: 30-year fixed at 6.25% with closing costs of $2900 and 1 point. Mortgage B: 30-year fixed at 4.5% with closing costs of $2900 and 2 points. Choose the correct answer below, and fill in the answer box to complete your choice.

Compare two mortgage options for a $155,000 loan with different interest rates (6.25% vs 4.5%), closing costs, and points. Learn how to calculate monthly payments, total interest, and determine which mortgage has the larger total cost.

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