The Hills obtain a 30-year, $144,000 conventional mortgage at a 4.5% rate on a house selling for $180,000. Their monthly mortgage payment, including principal and interest, is $729.63. They also pay 2 points at closing. Determine the total amount the Hills will pay for their house over 30 years.
30-year, $144,000 conventional mortgage at a 4.5% rate on a house selling for $180,000.
- Thread starter ginak
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Steven G
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I am no expert with these problems but I will give it a go.
I assume that if the loan was for $144,000 and the purchase price was $180,000 then a down payment of $36,000
They also pay $729.63 360 times which is $262666.80
I think that a point is $1,000 so 2 points will be $2,000
Just add up the underlined numbers
I assume that if the loan was for $144,000 and the purchase price was $180,000 then a down payment of $36,000
They also pay $729.63 360 times which is $262666.80
I think that a point is $1,000 so 2 points will be $2,000
Just add up the underlined numbers
Wish I could say same about you...
jonah2.0
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Beer soaked comments follow.
I feel however like filibustering.
In an effort to advertise low rates of interest, but still achieve high rates of return, lenders sometimes charge points. Each point is a 1% discount from the face value of the loan. In the Hills' case, a house is being sold for $180,000 and that the Hills pays $36,000 down and gets a $144,000, 30-year mortgage at a nominal (yearly) interest rate of 4.5% which is compounded (payable, convertible) 12 times per year (monthly) from a lender who charges 2 points.
A more worrying question then is the true interest rate on the loan.
Accordingly, the lender will advance 98% of $144,000, or $141,120. However, the monthly payment is calculated on the basis of a $144,000 loan:
144,000=R[1-(1+.045/12)^(-30*12)]/(.045/12)
←→144,000=R[1-(1.00375)^(-30*12)]/(.00375)
→ R=$729.63
Thus, the true monthly interest i is the solution of the equation
141,120=729.63[1-(1+i)^(-30*12)]/i
which is i=0.00389433126
The true interest rate on the mortgage loan is then 12i or .04673197512... or 4.6732% compounded monthly.
Points are charged at the beginning of the mortgage loan. Borrowers who decide to pay off their mortgage loan ahead of time will not recover any part of this charge. As a result, they will actually pay an even higher interest rate, if say the Hills decide to sell their house at the end of 5 years and pay off their mortgage.
That answer should should be sufficient.
I feel however like filibustering.
In an effort to advertise low rates of interest, but still achieve high rates of return, lenders sometimes charge points. Each point is a 1% discount from the face value of the loan. In the Hills' case, a house is being sold for $180,000 and that the Hills pays $36,000 down and gets a $144,000, 30-year mortgage at a nominal (yearly) interest rate of 4.5% which is compounded (payable, convertible) 12 times per year (monthly) from a lender who charges 2 points.
A more worrying question then is the true interest rate on the loan.
Accordingly, the lender will advance 98% of $144,000, or $141,120. However, the monthly payment is calculated on the basis of a $144,000 loan:
144,000=R[1-(1+.045/12)^(-30*12)]/(.045/12)
←→144,000=R[1-(1.00375)^(-30*12)]/(.00375)
→ R=$729.63
Thus, the true monthly interest i is the solution of the equation
141,120=729.63[1-(1+i)^(-30*12)]/i
which is i=0.00389433126
The true interest rate on the mortgage loan is then 12i or .04673197512... or 4.6732% compounded monthly.
Points are charged at the beginning of the mortgage loan. Borrowers who decide to pay off their mortgage loan ahead of time will not recover any part of this charge. As a result, they will actually pay an even higher interest rate, if say the Hills decide to sell their house at the end of 5 years and pay off their mortgage.