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    I get that there's a formula to calculate compound interest and that you can work out the amount you have left over a number of years with it. But what do I do when the number of years is a fraction?

    The question is - I invest £100 in a bank at a compound interest rate of 5% a year. What will the investment be worth in 2 and a half years?

    I'd really like it if someone could help
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    (Original post by abbie_)
    I get that there's a formula to calculate compound interest and that you can work out the amount you have left over a number of years with it. But what do I do when the number of years is a fraction?

    The question is - I invest £100 in a bank at a compound interest rate of 5% a year. What will the investment be worth in 2 and a half years?

    I'd really like it if someone could help
    There are in theory a number of different ways the interest could be compounded - e.g. the annual interest rate could be divided by 12 and then applied monthly. Or, your bank's systems could calculate interest on a daily basis which accrues to the stated annual rate!

    If you are asking about a "real" situation then you should probably ask your bank how they calculate the interest!
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    (Original post by davros)
    There are in theory a number of different ways the interest could be compounded - e.g. the annual interest rate could be divided by 12 and then applied monthly. Or, your bank's systems could calculate interest on a daily basis which accrues to the stated annual rate!

    If you are asking about a "real" situation then you should probably ask your bank how they calculate the interest!
    No, it's not a real situation!

    First of all, I used the P(1+R/100)^n formula, which has always been pretty good.

    But, obviously I can't just put the n as 2 and a half, because my interest is yearly? So I was wondering if there is another specific formula which would allow n to be a fraction?
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    This comes down to, what monthly interest rate r_m is equivalent over 12 months to annual rate r_a.
    Well
    (1+r_m)^{12}=r_a+1\\

1+r_m=(1+r_a)^\frac{1}{12}\\

r_m=(1+r_a)^\frac{1}{12}-1
    so if you have annual rate 5% this gives
    r_m=1.05^\frac{1}{12}-1=0.00407412
    Which is a monthly rate of 0.407412%.
    So for your part year, just use that monthly compound rate over the number of months involved.

    There are some interesting problems associated with this, here is an example. For a loan of £150000 at 4%.
    Given that the interest is calculated daily (a common scenario) and payments are monthly (usual) what monthly payment will mean that my payment in the last month of the 25th year. (i.e. the 300th payment) pays of the loan exactly?
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    (Original post by abbie_)
    I get that there's a formula to calculate compound interest and that you can work out the amount you have left over a number of years with it. But what do I do when the number of years is a fraction?

    The question is - I invest £100 in a bank at a compound interest rate of 5% a year. What will the investment be worth in 2 and a half years?

    I'd really like it if someone could help
    Simple. An investment of I pounds with an annual interest rate of k% will be worth

    I \times (1+\frac{k}{100})^n

    after n years, where n can be a fraction
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    (Original post by Indeterminate)
    Simple. An investment of I pounds with an annual interest rate of k% will be worth

    I \times (1+\frac{k}{100})^n

    after n years, where n can be a fraction
    n can be a fraction? That's fab! Thank you

    But in reality, would the bank give you the annual interest rate, if you remove your money half way throughout the year?


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    (Original post by abbie_)
    n can be a fraction? That's fab! Thank you

    But in reality, would the bank give you the annual interest rate, if you remove your money half way throughout the year?


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    You'd probably get half the interest as nothing will be left to pay interest on in the 2nd half, but check with the bank in question
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    There is no bank in question, I'm just wondering.. Just in case a more complicated question came up where they tried to trick me or something


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    You would not be given this at GCSE but it is worth knowing that banks charge daily.
    It used to be the case that if you overpaid on your normal monthly payment, the extra did not count against your amount owed until it was added on at the end of the year. This was a combination of the banks being greedy and the limited power of the IT available. More the greedy bit IMHO because if you underpaid, they seemed to be able to latch on to charging you extra interest with immediate effect.
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    (Original post by nerak99)
    You would not be given this at GCSE but it is worth knowing that banks charge daily.
    It used to be the case that if you overpaid on your normal monthly payment, the extra did not count against your amount owed until it was added on at the end of the year. This was a combination of the banks being greedy and the limited power of the IT available. More the greedy bit IMHO because if you underpaid, they seemed to be able to latch on to charging you extra interest with immediate effect.
    I'm not doing GCSE, but thank you for explaining


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