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Sagot :
Answer:
B
- a. down payment: $31,500
- b. amount of mortgage: $178,500
- c. points paid at closing: $1785
- d. total cost of interest over 30 years: $227,667
Step-by-step explanation:
You want to know the 15% down payment, the mortgage amount, the value of 1 point, and the total interest cost for a 6.5% 30 year loan on a $210,000 home.
Look at the Answer Choices
The answer choices all have the down payment as $31,500 and the loan value as $178,500. A "point" is one percent of the loan value (not the home value), so ...
1 point = 0.01 × $178,500 = $1785 . . . . . . eliminates choices A and C
The difference between choices B and D is in the value of the interest paid. Your experience with 30-year loans in this interest rate range tells you that the interest paid is between 1 and 2 times the loan value. That is, the chice $227,667 is more likely correct than the choice $406,167.
Comparing these two numbers, we see they differ by 178,500, which is the value of the loan. That is, we can guess that 406,167 is the total amount repaid, not just the interest.
Answer choice B is the only one that makes sense.
Work the problem
If you like, you can work the problem.
down payment = 15% × $210,000 = $31,500
loan amount = $210,000 -31,500 = $178,500
one point = 0.01 × $178,500 = $1785
The monthly payment is found using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
A = 178500(0.065/12)/(1 -(1 +0.065/12)^(-12·30)) ≈ 1128.24
The monthly payment amount is about $1128.
So, the total repaid is 360 payments of $1128.24, or $406,167.
The interest paid is this amount less the principal:
interest paid = $406,167 -178,500 = $227,667
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