Small Calculation-Need Help
 07-30-2009, 09:52 AM #1 Confused about dryer sheets   Join Date: Jul 2009 Posts: 1 Small Calculation-Need Help Hello all, I have a financial question and I hope you can help me. Assume the following situation: The after-tax return required to accumulate £2 million in 18 years beginning with an investable base of £1,235,000 and with annual outflows of £26,000 is 4.427 percent, which when adjusted for the 40 percent tax rate, results in a 7.38 percent pretax return (4.427%/(1 − 0.04) = 7.38%). I understand the Tax adjustment calculation. But how do you derive the 4.427 in the first place? I would really appreciate your help so I can understand the calculation! Many thanks in advance! Cheers, Peter __________________ __________________
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 07-30-2009, 10:25 AM #2 Give me a museum and I'll fill it. (Picasso) Give me a forum ...   Join Date: Jun 2002 Location: Texas Hill Country Posts: 42,099 Peter, in what part of South Africa is Arizona located? You might have better results at mathhomeworkhotline.com __________________ __________________ Numbers is hard When I hit 70, it hit back Retired in 2005 at age 58, no pension
 07-30-2009, 11:03 AM #3 Recycles dryer sheets   Join Date: Sep 2008 Posts: 60 I don't have a financial calculator nearby and didn't find one quickly on the Internet, but to get the necssary interest rate I would start with trying these numbers. N = 18 periods (I assume this is yearly compounding, would need to be adjusted if compounding is more frequent.) PV = -1,235,000 FV = 2,000,000 PMT = 26,000 i = _________ __________________
 07-30-2009, 11:23 AM #4 Recycles dryer sheets   Join Date: Jan 2009 Posts: 190 If you're just trying to "understand" it, your balance at any given year equals the balance of the previous year, times your rate of return that year, minus 26000. Now calculate that out for each year and you'll see your 2000000 balance after year 18. If there was no annual withdrawal, you can calculate it with: final balance = P(1+r)^y where P is the original amount, r the annual rate of return and y the number of years. Taking out money each year makes the equation really messy though, so it's easier to calculate iteratively like above. __________________
 07-31-2009, 02:28 PM #5 Thinks s/he gets paid by the post   Join Date: Jan 2006 Posts: 2,928 No idea why this is in Health and Retirement............ copy of Excel spreadsheet showing yr, begin balance, end balance before withdrawal, end balance after withdrawal, as suggested by K. Rate looks like a little over 4.425% so close to OP's. btw....slight decimal error in formula for BT return (denominator should be (1-0.4)? edit: sorry format did not take well but hopefully you can figure it out. rate0.04425 Begin end b w/d end a w/d1 1235.00 1289.65 1263.65 2 1263.65 1319.57 1293.57 3 1293.57 1350.81 1324.81 4 1324.81 1383.43 1357.43 5 1357.43 1417.49 1391.49 6 1391.49 1453.07 1427.07 7 1427.07 1490.22 1464.22 8 1464.22 1529.01 1503.01 9 1503.01 1569.52 1543.52 10 1543.52 1611.82 1585.82 11 1585.82 1655.99 1629.99 12 1629.99 1702.12 1676.12 13 1676.12 1750.28 1724.28 14 1724.28 1800.58 1774.58 15 1774.58 1853.11 1827.11 16 1827.11 1907.96 1881.96 17 1881.96 1965.23 1939.23 18 1939.23 2025.05 1999.05 __________________

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