Results 1 to 2 of 2

Math Help - Mortgage

  1. #1
    Len
    Len is offline
    Member
    Joined
    Mar 2008
    Posts
    93
    Thanks
    1

    Mortgage

    A couple buys a home and signs a mortgage contract for $200,000 to be paid with monthly payments over a 25-year period at i^(2) = 0.04.

    What is the monthly payment?

    n=25*12

    The confusing part for me is the interest rate, how do I know which one to use?

    I'm thinking I have to convert i^(2) to i^(12) then use j=i^(12)/12.


    Is there a quick relationship I can use to convert the interest rate? Currently I'm converting i^(2) to annual interest rate then back to i^(12)

    K* annuity(n)j = 200 000 and solve for K
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jul 2011
    Posts
    196

    Re: Mortgage

    Assuming i^(2) means your rate per period, which is twice a year, that would mean your j_{2} rate = 8%.

    You need to use an interest rate that is compounded with the same frequency as your regular payments.

    To convert from a semiannual (twice a year) interest rate, to an equivalent monthly interest rate simply set up the following equation:

    (1+\frac{0.08}{2})^2 = (1+\frac{j_{12}}{12})^{12}

    solving for j_{12}:

    (1.04)^{\frac{2}{12}}=1+\frac{j{12}}{12}

    j_{12} = 12\times ((1.02)^{\frac{2}{12}}-1)

     = 7.869836324%

    A good way to check that you have calculated the new interest rate correctly is to compare it to your original one. Because monthly rates compound more often than semiannual rates, in order for the two to be equal as an annual rate, the monthly rate should be slightly less than the 8% rate used when compounding twice a year.

    j_{12} = 7.869836324% which is slightly less than 8%

    Remember that the 8% and 7.869836324% are the annual rates so divide by the number of time periods before you use them. The monthly interest rate you will be using for your loan repayments will be \frac{7.869836324}{12}. Also, make sure to use your calculator and store the value you get for your interest rate - don't ever round it off.
    Last edited by terrorsquid; November 22nd 2011 at 02:47 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. mortgage
    Posted in the Business Math Forum
    Replies: 1
    Last Post: June 16th 2011, 10:50 PM
  2. Mortgage Formula
    Posted in the Business Math Forum
    Replies: 4
    Last Post: April 27th 2010, 11:22 AM
  3. Mortgage.
    Posted in the Business Math Forum
    Replies: 5
    Last Post: May 17th 2009, 05:25 PM
  4. Foreign mortgage - help please
    Posted in the Business Math Forum
    Replies: 1
    Last Post: April 9th 2009, 08:39 PM
  5. mortgage help please
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: April 10th 2008, 07:23 PM

Search Tags


/mathhelpforum @mathhelpforum