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Inflation-complicated compound interest

  1. Jan 7, 2009 #1
    Hi gang, I need help with a formula if somebody with an enormous brain and generous heart has some spare time.

    I need to work out what 9% of $60,000 ($5400) invested annual at 7% (net of fees and taxes) would grow to in 30 years, with the $60,000 increasing by 3% inflation each year (so the figure that 9% amounts to grows each year).

    There is also a starting balance of $100,000.

    I then need to be able to alter that 9% and make it 12% to see what the difference would be in the result.

    If anybody can help a maths knucklehead such as myself that would be wonderful.

    Thanks ... Nick.
     
  2. jcsd
  3. Jan 7, 2009 #2

    CRGreathouse

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    I don't think I understand the statement of the problem. Are you looking for the nominal or the real amount? Is 3% the inflation rate -- because in the problem it sounds like a COLA? What is the $100,000 starting amount -- does it include the $60,000 or not? If so, what happens with the other $40,000, is it invested at the risk-free rate (which is what?)?
     
  4. Jan 7, 2009 #3
    Hi CR, I didn't explain myself very well.

    In Australia, we have compulsory retirement savings of 9% of our annual wage ($60,000 in my example).

    I'm trying to work out what those contributions would grow in 30 years, given 7% returns (for simplicity, net of fees and taxes) a year and, critically, with the annual wage (again, $60, 000 in my example) rising each year in line with inflation of 3%pa, so that the 9% compulsory amount increases too each year.

    I then want to change the 9% to 12% to compare how tipping in each year an amount extra to the compulsory 9% would effect the result (that is, the investment balance).

    The $100,000 would be the retirement account balance when the retirement investor switched from 9% of annual wage to 12%.

    I know how to work out the FV of $5400 (9% of $60,000) invested at 7% for 30 years. What I don't know is how to do is allow for the $5400 to increase each year in line with inflation.

    I'd really love it if you knew a formula for this that I could punch into google calc.

    Thanks CR. I hope I haven't just made it much more confusing! ... Nick.
     
  5. Jan 7, 2009 #4

    CRGreathouse

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    The easy way, then, is to divide everything by 1.03 each year so you're working in real (not nominal) terms. Thus you get 3.88% after-inflation returns (1.07/1.03 - 1) and your contribution stays at $5400 inflation-adjusted dollars.
     
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