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Financial Mathematics

  1. Nov 9, 2005 #1
    Hod do you find the annual effective rate of interest?

    The question reads: You lend a freind $15 000 to be amortized by semiannual payments for 8 years, with interest at j2 = 9%. You deposit each payment in an account paying J12 = 7%. What annual effective rate of interest have you earned over the entire 8-year period?
    Ans = 8.17%

    Hmmm... i have absolutly no idea how to get the annuale effective rate of interest.

    My TA showed, (in another question) that its something like (1 + i)^n = 1 + r
    and solve for r?

    Please help somebody

    Thanks
     
  2. jcsd
  3. Nov 11, 2005 #2

    Fermat

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    The lender has invested $15 000 over an 8-year period. What will his $15 000 have become at the end of the 8 years ?

    Do you know how to calculate the Return on a Principle sum earning interest at r% pa over a term of n years ?
    In your lender's case, $15 000 is the Principle, you have yet to work out the Return, n is 8 years, and r would be the annual effective rate of interest that you have to find.

    The first part is a simple repayment scheme.
    A borrower gets a loan of $15 000 to be repaid in 16 semi-annual instalments.
    The annual rate for the loan is 9%. What is his repayment every six months ?
    Have you done loan repaymant schemes ?

    The 2nd part is the actual (rather than the effective) investment.
    The lender recieves R (the borrrower's six-monthly repayment value) every 6 months and immediately puts it into an account earning 7% annual interest.
    He does this for 8 years. How much money (the Return) willl be in the account at the end of that time ?

    Now that you have found the Return, you can work out the effective annual interest rate.
     
  4. Nov 11, 2005 #3

    hotvette

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  5. Nov 12, 2005 #4

    Fermat

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    Ah, thanks. Didn't notice that post.
    Seems our op wasn't too sure which forum his query should go in, so opted to use both of 'em :smile:

    btw, in your post, you mention "The payments that come in annually ..."
    Those payments should be semi-annual.
     
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