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compound interest-how do I work it out?

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budgetflyer
budgetflyer Posts: 5,949 Forumite
in Savings & investments
How do I work out the total
of say £10 per week for 10 years @ 5% PA?
keep it simple please
«1

Comments

  • grumbler
    grumbler Posts: 58,629 Forumite
    Part of the Furniture 10,000 Posts Name Dropper Photogenic
    I assume that 5% is AER
    365*10/7=521 weeks
    q=1.05^(1/52)
    £10*(q+q^2+q^3+…+q^521)=£10*q*(q^521-1)/(q-1)=£6722 :) (before taxes)
  • Paul_Varjak
    Paul_Varjak Posts: 4,627 Forumite
    Part of the Furniture 1,000 Posts Photogenic Combo Breaker
    Why not try an on-line financial calculator?

    http://www.moneymatterstome.co.uk/Interactive-Tools/GeneralInterestCalculator.htm


    There are many more on-line calculators. Just do a Google search to find the one you prefer.
  • lipidicman
    lipidicman Posts: 2,598 Forumite
    Nice method grumbler, good to see people using the correct way (ie ^(1/52))

    I usually do it iteratively in excel - I had forgotten that you can use the series expansion to simplify it!
    grumbler wrote:
    £10*(q+q^2+q^3+…+q^521)=£10*q*(q^521-1)/(q-1)=£6722
  • System
    System Posts: 178,343 Community Admin
    10,000 Posts Photogenic Name Dropper
    I really miss Digging_Out being around, he used to do my sums for me.
    This is a system account and does not represent a real person. To contact the Forum Team email forumteam@moneysavingexpert.com
  • grumbler
    grumbler Posts: 58,629 Forumite
    Part of the Furniture 10,000 Posts Name Dropper Photogenic
    lipidicman wrote:
    Nice method ... good to see people using the correct way (ie ^(1/52))
    Thank you for approval! I feel really flattered :o :beer:
    I always was a studious pupil... :rolleyes:
  • budgetflyer
    budgetflyer Posts: 5,949 Forumite
    grumbler wrote:
    I assume that 5% is AER
    365*10/7=521 weeks
    q=1.05^(1/52)
    £10*(q+q^2+q^3+…+q^521)=£10*q*(q^521-1)/(q-1)=£6722 :) (before taxes)

    not too simple :eek:
    Paul_Varjak wrote:
    Why not try an on-line financial calculator?

    http://www.moneymatterstome.co.uk/I...tCalculator.htm )

    thanks for that
  • lipidicman
    lipidicman Posts: 2,598 Forumite
    budgetflyer wrote:
    not too simple :eek:

    That is the simplest way to do it correctly!
  • grumbler
    grumbler Posts: 58,629 Forumite
    Part of the Furniture 10,000 Posts Name Dropper Photogenic
    budgetflyer wrote:
    not too simple
    What can be simpler than to put your numbers into the ready-made formula A*q*(q^N-1)/(q-1)? :confused: I am sorry, but you definitely are a poor hand at figures... :eek:
  • lipidicman
    lipidicman Posts: 2,598 Forumite
    As I have said I agree!

    could you just clarify that by q^N-1 you mean (q^N)-1 not q^(N-1)
    (it is correct without brackets if you do - the brackets just make it a little clearer when you have to use ^ rather than proper superscript notation)

    Also, where did you come across the simplification of q + q^2 + q^3+ q^4..... to get the final formula? Im have to verfied it, but havent found a derivation!
  • grumbler
    grumbler Posts: 58,629 Forumite
    Part of the Furniture 10,000 Posts Name Dropper Photogenic
    Yes
    A*q*(q^N-1)/(q-1) means A*q*[(q^N)-1)]/(q-1)
    However, the first expression is perfectly correct as 'power' has the higher priority than multiplicatin/division and addition/substraction. This experssion can be directly used in EXCEL without extra brackets. Actually the known BODMAS rule should be BPDMAS:
    Bracets
    Power
    Divisoin
    Multiplication
    Addition
    Subtraction

    See What on earth is BODMAS? :think:
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