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Math Help - Annual Payment

  1. #1
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    Question Annual Payment

    Hi, this is related to business, as its in the quantitative papers.

    You are paying off a 10,000 loan in 24 yearly instalments. You are charged 5% per annum. What should your annual payment be to the nearest pound?

    Is there a formula for working this out? I cant seem to find the answer. Is it possible to tell me how to work this out? and the answer as well?

    Many thanks!
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  2. #2
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    P = Ai / (1 - x) where x = 1 / (1 + i)^n

    P = Payment (?)
    A = Amount borrowed (10,000)
    i = interest rate (.05)
    n = number of years (24)

    Yokay?
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  3. #3
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    Smile

    Hi, thanks for the reply. So its done like this:

    P = Ai / (1 - x) where x = 1 / (1 + i)^n

    P = Payment (?)
    A = Amount borrowed (10,000)
    i = interest rate (.05)
    n = number of years (24)

    P= (10,000*.05)/(1-0.3100679103)=
    500/0.6899320897=724.71, and round it up is 725.

    Hey, thanks there!

    -
    Find out x, so 1/(1+.05)^24=1/(1.05)^24=3.225099944, then 1/3.225099944=0.3100679103. Then thats the answer for x.
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  4. #4
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    Yep.
    And if you wanted 24 months instead of 24 years, then:
    10000(.05/12) / [1 - 1/(1 + .05/12)^24] = 438.71
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  5. #5
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    Cheers! would take note of that. how do u remember all these formulas by heart? its so hard, lol.

    why do u need certain formulas for it? and how do u know immediately?
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