If the terms at Chase Bank are a 10% down payment, an interest rate of 4%, a 30-year conventional mortgage and 3 points to be pa

Question

3 years ago

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If the terms at Chase Bank are a 10% down payment, an interest rate of 4%, a 30-year conventional mortgage and 3 points to be pa

id at the time of closing, calculate the total amount needed at the time of closing, the monthly payment, and the total cost paid for the home. The house is 105,000. Please show work or give the steps as to how you did it.

Mathematics

1 answer:

dangina [55] · Answer 1 · 2022-03-27T12:37:45+03:00

Answer:

closing cost: $13,335
payment: $451.16
total cost: $175,751.68

Step-by-step explanation:

Step 1 - compute the down payment

10% × $105,000 = $10,500

Step 2 - compute the loan amount

$105,000 -10,500 = $94,500

Step 3 - compute the cost of the loan and closing costs

The cost of the loan is 3% of the loan value:

3% × $94,500 = $2835

This amount added to the down payment gives the closing costs:

closing cost = $10,500 +2,835 = $13,335

Step 4 - compute the monthly payment

For this, we use the amortization formula for payment A on principal P at interest rate r for n years:

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

A = $94,500(.04/12)/(1 -(1 +.04/12)^(-12×30)) ≈ $451.16 = monthly payment

Step 5 - compute the amount repaid on the loan

total of payments = 30×12×$451.16 ≈ $162,416.68

For this calculation, we use the full-precision value of the loan payment, not the value rounded to cents found in step 3. Doing that approximates the effect of the adjustment that will be made in the final payment of the loan.

Step 6 - find the total cost of the home

The loan repayment amount is added to the closing costs:

$162,416.68 +13,335 = $175,751.68 = total cost paid

_____

Comment on Step 5

You may find the required answer for total repayment amount is $0.92 higher, $175,752.60. The total amount of 360 payments of 451.16 is $162,417.60, which is higher than the amount shown above in Step 5.

Since the monthly payment amount is rounded up to the nearest penny, loan repayment is actually very slightly faster, so the final payment does not need to be the full amount of $451.16. In real life, the bank will let you know the final payment amount, or will refund the difference after the last payment.