Running out of TFLS

Moonwolf

Morning I should know this but my maths is failing me.

I'm looking for the formula that resolves x(1+r)^1+x(1+r)^2+x(1+r)^3...x(1+r)^n

This is an expansion of x*(1+r)t

Where x is a sum (in this case the tax free part of drawdown) and r is the rate (interest) and t is time period. 

I've tried googling but nowadays I get an AI solution that is patently wrong.

I've realised that while I work in real terms and ignore inflation there is a case where it doesn't work. 

The tax thresholds aren't moving with inflation and while my plans have my income well under the 40% threshold at the moment, depending on inflation, it might get there before the higher rate threshold changes.  However I will still be under if I am drawing down UFPLS style as the first 25% will be tax free.

That then raises the question, when might I run out of TFLS allowance?  I'm assuming this will not change with inflation ever so just shrink in value (of course, future governments might realign it with inflation or take it away entirely). So I wanted to play with different inflation rates and see when I might run out.  I think the formula above should do it and I have the clunky version of a row for each year in my spreadsheet which works anyway as my drawdown rate is not consistent.

However, that should resolve to a single formula that takes tax free amount drawn down each year, choose and interest rate and then I can see when it reaches £268,275

Cobbler_tone

Moonwolf said:

I'm looking for the formula that resolves x(1+r)^1+x(1+r)^2+x(1+r)^3...x(1+r)^n

You lost me at this point. 

Moonwolf

Cobbler_tone said:

Moonwolf said:

I'm looking for the formula that resolves x(1+r)^1+x(1+r)^2+x(1+r)^3...x(1+r)^n

You lost me at this point. 

I probably wrote it badly.

For annual interest if you want to know what £x will be worth in t years time when inflation is r you can just use the formula

x * (1+r)^t  ^t is raised to the power

So £100 in 20 years at 2% inflation will be worth  200*(1+.02)^20  which is £100 * 1.4859 or £148.59

I want to know £5000 + (£5000 + 1 years inflation) + (£5000 + 2 years inflation) and so on, I actually want to know how long it takes to £268,275 at different inflation rates. 

I know that can be reduced to a formula but I can't remember the formula and more embarrassingly I can't remember how to work it out, which should be in my skillset.

Linton

Moonwolf said:

Morning I should know this but my maths is failing me.

I'm looking for the formula that resolves x(1+r)^1+x(1+r)^2+x(1+r)^3...x(1+r)^n

This is an expansion of x*(1+r)t

Where x is a sum (in this case the tax free part of drawdown) and r is the rate (interest) and t is time period. 

I've tried googling but nowadays I get an AI solution that is patently wrong.

I've realised that while I work in real terms and ignore inflation there is a case where it doesn't work. 

The tax thresholds aren't moving with inflation and while my plans have my income well under the 40% threshold at the moment, depending on inflation, it might get there before the higher rate threshold changes.  However I will still be under if I am drawing down UFPLS style as the first 25% will be tax free.

That then raises the question, when might I run out of TFLS allowance?  I'm assuming this will not change with inflation ever so just shrink in value (of course, future governments might realign it with inflation or take it away entirely). So I wanted to play with different inflation rates and see when I might run out.  I think the formula above should do it and I have the clunky version of a row for each year in my spreadsheet which works anyway as my drawdown rate is not consistent.

However, that should resolve to a single formula that takes tax free amount drawn down each year, choose and interest rate and then I can see when it reaches £268,275

I think your maths is wrong...

After 1 year 25% of your pot is x*(1+r).  After 2 years it is x*(1+r)*(1+r)= x*(1+r)^2 etc where r is the fractional return and x 25% of your initial pot size.  Your formula adds an extra x for each term. 
  

For your simple case you can just work in current value and reduce r by expected long term inflation.  To deal with more complicated circumstances you have no option other than using a year by year spreadsheet.  That is probably the easiest way of playing with the numbers anyway.

Moonwolf

Linton said:

Moonwolf said:

Morning I should know this but my maths is failing me.

I'm looking for the formula that resolves x(1+r)^1+x(1+r)^2+x(1+r)^3...x(1+r)^n

This is an expansion of x*(1+r)t

Where x is a sum (in this case the tax free part of drawdown) and r is the rate (interest) and t is time period. 

I've tried googling but nowadays I get an AI solution that is patently wrong.

I've realised that while I work in real terms and ignore inflation there is a case where it doesn't work. 

The tax thresholds aren't moving with inflation and while my plans have my income well under the 40% threshold at the moment, depending on inflation, it might get there before the higher rate threshold changes.  However I will still be under if I am drawing down UFPLS style as the first 25% will be tax free.

That then raises the question, when might I run out of TFLS allowance?  I'm assuming this will not change with inflation ever so just shrink in value (of course, future governments might realign it with inflation or take it away entirely). So I wanted to play with different inflation rates and see when I might run out.  I think the formula above should do it and I have the clunky version of a row for each year in my spreadsheet which works anyway as my drawdown rate is not consistent.

However, that should resolve to a single formula that takes tax free amount drawn down each year, choose and interest rate and then I can see when it reaches £268,275

I think your maths is wrong...

After 1 year 25% of your pot is x*(1+r).  After 2 years it is x*(1+r)*(1+r)= x*(1+r)^2 etc where r is the fractional return and x 25% of your initial pot size.  Your formula adds an extra x for each term. 
  

For your simple case you can just work in current value and reduce r by expected long term inflation.  To deal with more complicated circumstances you have no option other than using a year by year spreadsheet.  That is probably the easiest way of playing with the numbers anyway.

That is the intention, I'm after the cumulative amount of tax free drawn down. In the first year I might draw down £20k of which £5000 is tax free so I will have used that much of my £268k allowance.  At 2% inflation, in the second I will draw down with an inflation uplift so £5100 from the allowance, the third year £5404, so by then £15,504 from the £268,275 allowance, which I'm assuming hasn't risen with inflation. 

At what point do my cumulative withdrawals mean I have no tax free allowance left and might have to reduce my drawdown or assume I am paying some 40% tax, either way I'll have a bit less "take home".  It looks like in my late 80s or 90s in my case, so probably fine anyway.  I note that James Shack tends to reduce spending around 75.

LHW99

I think the equation may be something like:

No idea on the maths itself though

Linton

Moonwolf said:

Linton said:

Moonwolf said:

Morning I should know this but my maths is failing me.

I'm looking for the formula that resolves x(1+r)^1+x(1+r)^2+x(1+r)^3...x(1+r)^n

This is an expansion of x*(1+r)t

Where x is a sum (in this case the tax free part of drawdown) and r is the rate (interest) and t is time period. 

I've tried googling but nowadays I get an AI solution that is patently wrong.

I've realised that while I work in real terms and ignore inflation there is a case where it doesn't work. 

The tax thresholds aren't moving with inflation and while my plans have my income well under the 40% threshold at the moment, depending on inflation, it might get there before the higher rate threshold changes.  However I will still be under if I am drawing down UFPLS style as the first 25% will be tax free.

That then raises the question, when might I run out of TFLS allowance?  I'm assuming this will not change with inflation ever so just shrink in value (of course, future governments might realign it with inflation or take it away entirely). So I wanted to play with different inflation rates and see when I might run out.  I think the formula above should do it and I have the clunky version of a row for each year in my spreadsheet which works anyway as my drawdown rate is not consistent.

However, that should resolve to a single formula that takes tax free amount drawn down each year, choose and interest rate and then I can see when it reaches £268,275

I think your maths is wrong...

After 1 year 25% of your pot is x*(1+r).  After 2 years it is x*(1+r)*(1+r)= x*(1+r)^2 etc where r is the fractional return and x 25% of your initial pot size.  Your formula adds an extra x for each term. 
  

For your simple case you can just work in current value and reduce r by expected long term inflation.  To deal with more complicated circumstances you have no option other than using a year by year spreadsheet.  That is probably the easiest way of playing with the numbers anyway.

That is the intention, I'm after the cumulative amount of tax free drawn down. In the first year I might draw down £20k of which £5000 is tax free so I will have used that much of my £268k allowance.  At 2% inflation, in the second I will draw down with an inflation uplift so £5100 from the allowance, the third year £5404, so by then £15,504 from the £268,275 allowance, which I'm assuming hasn't risen with inflation. 

At what point do my cumulative withdrawals mean I have no tax free allowance left and might have to reduce my drawdown or assume I am paying some 40% tax, either way I'll have a bit less "take home".  It looks like in my late 80s or 90s in my case, so probably fine anyway.  I note that James Shack tends to reduce spending around 75.

You are withdrawing T TFLS increasing with inflation I (plus the 75% taxable).  This is not linked to the amount of money in your pot which we can assume therefore is unlimited. 

Your total TFLS used over n years  T*(1+(1+I)+(1+I)^2 +...(1+I)^(n-1))
= I*((1+I)^n - 1)/((1+I)-1)
= T*((1+I)^n - 1)/I

So n, the number of years to use up the constrant TFLS limit, L is given by

L= T*((1+I)^n - 1)/I

Rearranging gives
L*I/T=(1+I)^n-1
(1+I)^n=1+L*I/T
n=log(1+L*I/T)/log(1+I)

So if T=5000, L=268275, and I=3%=0.03 we have:
n=log(2.60965)/log(1.03)
n=0.206/0.013
=32 years

Or as a sanity check let I=0.001

n=log(1.0535)/log(1.001)
=0.00226/0.000432
=52.3 years which is reassuringly close to 268275/5000=53.67

Moonwolf

Thanks, that is exactly what I was looking for.  

Obviously the total pot may never grow large anyway but it is an interesting exercise for anyone who's number is closer to 40%, is using UFPLS and relying on it not to pay 40% tax.

I should be OK unless inflation is very high and it looks like I am more likely to run out of pot than TFLS in most scenarios.  Which is essentially the question I was asking.

QrizB

I knew logarithms would be involved, but it's far too long since my O-level maths!

Secret2ndAccount

Use a spreadsheet. You can try multiple scenarios side by side, plot little graphs to compare, and use goal-seek if you want an exact solution

Hoenir

Moonwolf said:

Obviously the total pot may never grow large anyway but it is an interesting exercise for anyone who's number is closer to 40%, is using UFPLS and relying on it not to pay 40% tax.

My aim is to maximise withdrawls within the 20% tax band and fully utilise my annual ISA allowance. Any excess funds are being invested into low coupon Government Gilts within a GIA. With many allowances frozen for the foreseeble future. No need to get overly complex and try to forecast the unforecastable.