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Math Help - Choice of Two Options for Paying off a Loan

  1. #1
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    Choice of Two Options for Paying off a Loan

    "You can pay off a loan by paying the entire amount of £10,000 now or you can pay £5,000 now and £5,000 at the end of five years. Which is preferable when the nominal continuously compounded interest rate is:

    a. 2.5%
    b. 5%
    c. 7.5%"

    I thought this was a cash flow problem when I first looked at it but after going to the library and trying to read some finance books I have confused myself and think I am wrong and am not sure where to start. Is there anyone who can help me with part a (I will be able to do parts b and c if i can do part a!)?
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  2. #2
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    Unless the outstanding loan balance is compounding, it will always be best to defer the payment to a later date. That way, you can hang on to the money and allow it to compound, making money for you, before you have to give it up to someone else.

    The continuous compounding formula is:
    FV = Pe^(Yr)

    So, for part a we have: P=5000, Y=5, r=.025... plug it in and get FV=5665.74. This means that you could earn 665.74 over 5 years if you decided to keep the money and pay later, instead of paying now.
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  3. #3
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    When I looked at the question that's what I thought - that it would always be better to pay half now and half later and earn interst on the second half. Though with the seemingly being the case I do not understand why there are three interest options that you have to decide for. Any interest makes it worthwhile!

    Thanks for the reply and confirming what I thought to be the answer from reading the question!
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