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Financial Maths

  1. Aug 5, 2017 #1
    1. The problem statement, all variables and given/known data
    The problem ask to calculate the interest rate of a loan. The principal is $735 000, term is 25 years (300 months), and the repayments due is $4656.17/month.

    i = interest rate, PV = present value, R = repayments

    2. Relevant equations
    PV = R x [(1+i/12)^300 - 1]/(i/12)

    3. The attempt at a solution
    I managed to calculate the total interest to pay = $661 851
    735000 = 4656.17 x [(1+i/12)^300 - 1]/(i/12)
    13.155 = [(1+i/12)^300 - 1]/i
    13.155i = [(1+i/12)^300 - 1]
    13.155i + 1 = (1+i/12)^300
    I realised that this may not be correct but I have no idea of what to do. I put this into an online calculator and it gave a value of 5.823% but I don't know how it got to it. Please help.
     
  2. jcsd
  3. Aug 5, 2017 #2
    Hi I think you have written the formula of the future value. The present value would be $$\text{PV} = \frac{R}{(i/12)}\left[ 1 - \frac{1}{\left(1+\frac{i}{12}\right)^{300}} \right] $$ Now we can't solve this analytically, so use RATE function from Excel. I just checked the calculations, and I think your APR seems correct to me
     
  4. Aug 5, 2017 #3
    Thanks so much. I thought as much after a few hours that this was impossible to solve manually.
     
  5. Aug 5, 2017 #4
    Are you familiar with Newton's method for solving non-linear algebraic equations?
     
  6. Aug 5, 2017 #5
    What do you get if you expand ##\left(1+\frac{i}{12}\right)^{-300}## using the binomial expansion and retaining only the first three terms?
     
    Last edited: Aug 5, 2017
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