Question

A house is being purchased at the price of $138,000.00. The 30-year mortgage has a 10% down payment at an interest rate of 4.875% and a PMI payment of $25.88 each month for 77 months. The yearly taxes are $2400.00 and the insurance is $750.00 per year, which is to be placed into an escrow account. What is the total cost of the loan? Round your answer to the nearest one hundred dollars. Enter a number, such as $123,500.00.

Answer 1

The total cost of the loan is $249,300.00.

Step-by-step explanation:

To calculate the total cost of the loan, we need to add up the down payment, mortgage payments, PMI payments, taxes, and insurance. Here are the step-by-step calculations:

Down payment: 10% of $138,000.00 = $13,800.00

Mortgage amount: $138,000.00 - $13,800.00 = $124,200.00

Mortgage payment: Using a mortgage calculator, we can determine the monthly payment for a 30-year loan at 4.875% interest rate and a principal of $124,200.00. This comes out to $657.51 per month.

PMI payments: $25.88 per month for 77 months, which totals to $1,992.76.

Taxes: $2,400.00 per year, so over 30 years, it amounts to $72,000.00.

Insurance: $750.00 per year for 30 years adds up to $22,500.00.

Now, let's add up all the costs: $13,800.00 + ($657.51 x 360 months) + $1,992.76 + $72,000.00 + $22,500.00 = $249,326.36. Rounding to the nearest hundred dollars, the total cost of the loan is $249,300.00.

Answer 2

$238,600

Step-by-step explanation:

The amount being borrowed is 100% -10% = 90% of the purchase price, or ...

0.90 × $138,000 = $124,200.

Then the monthly payment can be computed using the amortization formula:

A = P(r/12)/(1 -(1 +r/12)^(-12t))

A = 124200(.04875/12)/(1 -(1 +.04875/12)^(-12·30)) ≈ 657.28

and the total repaid is ...

(360 months) × ($657.28/month) = $236,619.58*

The cost of mortgage insurance is considered part of the cost of the loan. That amount is ...

(77 months) × ($25.88/month) = $1992.76

so the total amount paid for the loan is ...

$236,619.58 +1992.76 = $238,612.34

The cost of the loan is about $238,600.

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* In figuring the total repayment cost, we used the full-precision value for the loan payment. The actual repayment amount will depend on the rounded value of the loan payment and the way the final payment is made. When rounded to the nearest $100, these details become unimportant.