Small Calculation-Need Help

[PeterF]

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

 

[REWahoo]

Peter, in what part of South Africa is Arizona located?

You might have better results at mathhomeworkhotline.com

 

[Uncle Drew]

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 = _________

 

[Kabekew]

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.

 

[kaneohe]

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.

rate​

0.04425​

Begin
end b w/d
end a w/d​

1
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​