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Math Help - Help with a question plz=)

  1. #1
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    Help with a question plz=)

    Hello,
    First off forgive my bad english. I will do my best to make this understandable.
    I'm preparing for a Real Estate exam and I'm having difficulties with the math. I only have an high school education and mathematics have never been my forte.

    I was presented with this question:

    When Branham brought his property he had a 20% down payment and
    secured a 30 year loan at 7% interest. If his first month’s interest was
    $787.50, how much did he pay for the property?
    A. $135,000
    B. $140,625
    C. $168,750
    D. $158,250


    I'm sure there must be a formula , given the percentage and monthly interest rates etc... , to calculate the solution?
    I figured that one of those prices had to be the right one. I tried to solve it but failed miserably.
    This is what I did and i was certain it was the right answear

    I started with B. $140.625. I figured Branham had a 20$ down payment so I did 20% of 140.625 , considering that B. was the price he paid for the house. Keep in mind i was going to do this for all the values (a b c d).
    Alright so 20% of 140.625 came to $28.125.
    I figured it was the right price but nope the right one was C.
    I also noticed that i had the answer in front of me the all time. I just had to add 28.125 to 140.625.
    I guess that 28.125 is the 20% deposit? If not then why when added to 140.625 it gives me the correct price.

    I'm lost.


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  2. #2
    MHF Contributor
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    67
    .07k / 12 = 787.50
    .07k = 12 * 787.50 = 9450
    k = 9450 / .07 = 135000 : this is the amount borrowed

    Purchase
    = 135000 / (1 - .20)
    = 135000 / .8
    = 168750
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  3. #3
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    Thanks Wilmer for the help.
    I understand now how to calculate the original price of the property but I'm still confused on one part of the question.

    It says "how much did he pay for the property?" I just don't understand how can i possibly answear this. $9450 a year of interests is the equivalent $283.500 at the end of the 30 year loan on interests alone. If it's an open mortgage/loan he can pay it off at any time but in that case the price of the house that he will be paying for it will vary depending on when he pays off the loan.
    If he keeps the loan for the 30 years term he will be paying the house $418.500 so how can i possibly guess work how much Mr. Branham will pay for that property?
    On an open mortgage he has the freedom to pay off the loan at any time he could pay it off at 5 year 15, 20 etc... and the final price will be different.
    Does it want to know the original price of the property before the interests or how much he will pay for that property at the end of the 30 year loan? lol
    Even if he paid $787.50 for the first month then he payed $168,750+$787,50(interests).
    It's either me or the question was not phrased properly.
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  4. #4
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    67
    168,750 : total purchase price
    -33,750 : down payment
    ======
    135,000 : amount of loan

    If he had enough "cash", he could have paid 168,750; then no need to get loan.

    The fact that he does not have enough cash and needs to borrow has NOTHING
    to do with "what he paid for house".

    The 135,000 loan will require monthly payments of 898.16 for 30 years (360 months);
    898.16 * 360 = 323,338 = total paid back
    323,338 - 135,000 = 188,338 = total interest on the loan
    Again, this interest has NOTHING to do with purchase price of house.

    IF you're looking for how much Mr B will pay out in total before house is fully paid,
    then it's 33,750 (down payment) + 323,338 (360 monthly payments) = 357,088
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  5. #5
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    Thanks again for help.
    I guess my english is what made things little more complicated for me.
    I understand what you mean when you say "The fact that he does not have enough cash and needs to borrow has NOTHING to do with "what he paid for house"."
    Since it's a loan from the bank that's what he's paying back.
    But when the question asks me "how much did he pay for the property" loan or not loan if he goes on for 30 years with the loan he has paid that property $357,088 like you said.
    Yes the property was paid tanks to the bank loan and the 20% down payment $168,750.
    But he still has to pay the loan back for 30 years and no matter wich way you want to look at it that loan was made for the house.
    So unless he pays off the loan earlyer he ended up paying that property $357,088.
    I'm just gona give up on anythign with math
    I just don't get it how they can say he payed that property $168,750 when he has a loan on it. Don't get me wrong I know what you mean but it's just doesn't make sense how one does not take in consideration the $188,338 ( total interest on loan) on the final price of the house.
    I mean it's not even correct at this point to say " how much did Mr. Branham pay for the property?" well he only put a down payment of 20%, that's how much he paid for it, the rest was a loan that will take him 30 years to pay for it.
    In other words the bank paid for the house and if he doesn't pay for the loan the bank will show Mr. branham who really owns the house=)
    I guess i take things a little to literary and i suck at math.
    It's just funny to me that if in real life i go up to somebody and ask them how much they paid for this property/ car etc.... they will just hit me with a riddle lol
    Well i paid for this house the following: " I put a 20% down payment and my first monthly interest rate was......" guess how much i paid for the house=)

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