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Math Help - Finding Interest paid. Help please

  1. #1
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    Finding Interest paid. Help please

    Hi, I would appreciate any help with the following exercise in financial maths. I'm a lawyer and I'm quite lost with the approximation technique to find the interest.

    The Problem:

    You borrow $ 1000 from a loan shark and are offered a choice of two possible loan repayment schemes:

    - 20 monthly repayments of $ 100, with the first repayment being one month after you borrow the $ 1000.

    - 10 monthly repayments of $80, with the first repayment being one month after you borrow the $ 1000 followed by a singl repayment of $800, 11 months after you borrow the $ 1000.

    The questions:

    a) Determine* the effective interest rate J12 that you are being charged in the first option.

    b) Determine* the effective interest rate J12 that you are being charged in the second option, and thus identify which of the two options is preferable.

    *Within an accuracy of +/- 1.2% which implies that you will need to find i to an accuracy of +/- 0.1%.


    Your help is much appreciated.

    Mauricio
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  2. #2
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    Quote Originally Posted by 10219929 View Post
    Hi, I would appreciate any help with the following exercise in financial maths. I'm a lawyer and I'm quite lost with the approximation technique to find the interest.

    The Problem:

    You borrow $ 1000 from a loan shark and are offered a choice of two possible loan repayment schemes:

    - 20 monthly repayments of $ 100, with the first repayment being one month after you borrow the $ 1000.

    - 10 monthly repayments of $80, with the first repayment being one month after you borrow the $ 1000 followed by a singl repayment of $800, 11 months after you borrow the $ 1000.

    The questions:

    a) Determine* the effective interest rate J12 that you are being charged in the first option.

    b) Determine* the effective interest rate J12 that you are being charged in the second option, and thus identify which of the two options is preferable.

    *Within an accuracy of +/- 1.2% which implies that you will need to find i to an accuracy of +/- 0.1%.


    Your help is much appreciated.

    Mauricio
    Hi. Can you use a spreadsheet here? There is an IRR function for Internal Rate of Return that can be used for this. If you create an array with the loan amount as a negative number followed by the payments as positive numbers, and plug that array into the IRR function, it will give you the monthly effective interest rate for that loan. I get monthly rates of 7.75% and 6.14% for (a) and (b).
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  3. #3
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    Question Thanks Jake but...

    Jake, because this is an assignment I have to show some procedures in my answers. What they want us to do is to use the iterative approach (replacing different values for i in the present value annuity formula:

    PV=R(1-(1+i)^-n/i

    I already did it with question 1 (20 payments of 100 to pay off 1000 loan).

    But I don't know where to start with question 2 (10 payments of 80 and 800 at the end on the eleventh period). I don't know how to manage the $800.

    If you have an idea I'd appreciate your help or anyone's else.

    Thanks,

    Mauricio
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  4. #4
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    Quote Originally Posted by 10219929 View Post
    Jake, because this is an assignment I have to show some procedures in my answers. What they want us to do is to use the iterative approach (replacing different values for i in the present value annuity formula:

    PV=R(1-(1+i)^-n/i

    I already did it with question 1 (20 payments of 100 to pay off 1000 loan).

    But I don't know where to start with question 2 (10 payments of 80 and 800 at the end on the eleventh period). I don't know how to manage the $800.

    If you have an idea I'd appreciate your help or anyone's else.

    Thanks,

    Mauricio
    Mauricio, it helps if you state what's required and what you've tried in your original question. It takes longer if we have to guess what you know and are supposed to do.

    You can add present values. So you can use the formula to calculate the PV of the 10 payments as a function of i. Then you can add the PV of 800 (which is 800/(1+i)^11) to get the total PV. Then you can iterate on i using the total PV the same as for question 1.

    JakeD
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