Let's solve this step-by-step.

Given Information:

• Asking price: $529,900
• You offered 93% of the asking price.

Problem 1: Calculate the purchase price

You offered 93% of the asking price, so the purchase price will be:

$\text{Purchase Price} = 0.93 \times 529,900$

$\text{Purchase Price} = 492,807$

The purchase price is $492,807.00.

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Problem 2: Calculate the down payment and loan amount

The bank requires a 20% down payment. This means the down payment is 20% of the purchase price, and the loan amount is the remaining 80%.

Down payment:

$\text{Down payment} = 0.20 \times 492,807 = 98,561.40$

Loan amount:

$\text{Loan amount} = 0.80 \times 492,807 = 394,245.60$

• Down payment: $98,561.40
• Loan amount: $394,245.60

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Problem 3: Calculate the closing costs and total upfront costs

The closing costs are 5% of the purchase price. The total upfront costs include both the down payment and the closing costs.

Closing cost:

$\text{Closing cost} = 0.05 \times 492,807 = 24,640.35$

Total upfront costs:

$\text{Total upfront} = \text{Down payment} + \text{Closing cost} = 98,561.40 + 24,640.35 = 123,201.75$

• Closing cost: $24,640.35
• Total upfront: $123,201.75

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Problem 4: Calculate the monthly mortgage payment

For a 30-year fixed-rate mortgage at an interest rate of 3.2%, we can use the mortgage payment formula:

$M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}$ Where:

• $M$ = monthly payment
• $P$ = loan amount = $394,245.60
• $r$ = monthly interest rate = $\frac{3.2}{12} = 0.00267$
• $n$ = number of months = 30 \times 12 = 360

Plugging in the values:

$M = 394,245.60 \times \frac{0.00267(1 + 0.00267)^{360}}{(1 + 0.00267)^{360} - 1}$

Using a calculator, we find:

$M \approx 1,707.98$

• Monthly payment: $1,707.98

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Problem 5: Calculate total cost and financing charges

Now, we'll calculate the total amount paid over 30 years and compare it to the purchase price to determine the total financing charges.

Total paid over 30 years:

The total paid is the sum of the monthly payments over 30 years, plus the closing costs and down payment.

$\text{Total paid} = \text{Monthly payment} \times 360 + \text{Total upfront}$

$\text{Total paid} = 1,707.98 \times 360 + 123,201.75 = 614,872.80 + 123,201.75 = 738,074.55$

Difference (financing charges):

The difference between the purchase price and the total amount paid is the total financing charges.

$\text{Financing charges} = 738,074.55 - 492,807 = 245,267.55$

• Total paid: $738,074.55
• Financing charges: $245,267.55

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Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What would the monthly payment be if the interest rate increased to 4%?
2. How much total interest is paid over the 30-year mortgage period?
3. What is the impact on the loan amount if you made a 25% down payment instead?
4. How much would you save on the total paid if the mortgage term was shortened to 15 years with the same interest rate?
5. What would be the new closing cost if the price of the house was negotiated down to $450,000?

Tip: It's always beneficial to understand the breakdown of upfront costs versus long-term financing to make informed financial decisions.