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
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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.
