Gross pension return equivalencing?
Discussion
Hi -
One for the maths whizz's:
If i have a gross return to my pension: i.e. I've paid in 'x' and the current value is 'x*1.15'
I've had the pension for 'y' years.
My gut feel is that this is a s
t return (15% over 5 years) but would like to see it equived over the period.
n.b. contributions are from months 48-66 35% higher than initially
One for the maths whizz's:
If i have a gross return to my pension: i.e. I've paid in 'x' and the current value is 'x*1.15'
I've had the pension for 'y' years.
My gut feel is that this is a s
t return (15% over 5 years) but would like to see it equived over the period.n.b. contributions are from months 48-66 35% higher than initially
Looked like a vaguely interesting problem so I've had a stab at it...
Assumptions (based on your post):
* You started paying in an amount "m" monthly, 66 months ago
* In month 48, you started paying "1.35m"
* The value of your fund today, at the end of month 66 (i.e. 5 and a half years) is 1.15 times your total payments, i.e. 1.15*(47m + 19*1.35m)
I believe that the answer is an AER of 5.5%.
Working out:
Let the monthly interest multiplier be "r" (e.g. 0.5% monthly would be 1.005). Then the AER multiplier should be r to the power of 12 (e.g. 1.062), and AER would be AER multiplier minus 1 (e.g. 6.2%). We want to solve for the actual value of "r".
After month 1, you have "m" in the pot.
After month 2, you have "m*r + m"
After month 3, you have "(m*r + m)*r + m" = "m*(r^2 + r + 1)"
etc.
After month 47, you have "m*(r^47 + r^46 + ... + r^2 + r + 1)"
After month 48, you have "m*(r^48 + r^47 + ... + r^3 + r^2 + r) + 1.35*m"
After month 66, you have "m*(r^66 + r^65 + ... + r^20 + r^19 + r^18) + 1.35*m*(r^17 + r^16 + ... + r^2 + r + 1)"
We then equate this with the total pot computed earlier (1.15*(47m + 19*1.35m)). The m's cancel on both sides, and we are left with an equation in r.
This is best solved in Excel - if you're into hand calculations, use interval bisection or something starting with the interval [1, 1.15] since we know the monthly interest rate is in between those two values. The answer comes out as r = 1.00449 or thereabouts.
Then r^12 gives 1.055 or 5.5% AER.
Whether this is a good return or not is another question altogether. Considering this period spans the financial crisis, along with low interest rate period, an average return of over 5% per year tax free actually looks pretty good to me. I think I'd keep paying in to a pension with that kind of return.
Usual disclaimers: All of the above may be wrong, I am not a financial adviser, etc etc.
Edited to correct a couple of numbers - specifically the assumption that 47 months were at "m" and 19 months (48-66 inclusive) were at "1.35m"
Assumptions (based on your post):
* You started paying in an amount "m" monthly, 66 months ago
* In month 48, you started paying "1.35m"
* The value of your fund today, at the end of month 66 (i.e. 5 and a half years) is 1.15 times your total payments, i.e. 1.15*(47m + 19*1.35m)
I believe that the answer is an AER of 5.5%.
Working out:
Let the monthly interest multiplier be "r" (e.g. 0.5% monthly would be 1.005). Then the AER multiplier should be r to the power of 12 (e.g. 1.062), and AER would be AER multiplier minus 1 (e.g. 6.2%). We want to solve for the actual value of "r".
After month 1, you have "m" in the pot.
After month 2, you have "m*r + m"
After month 3, you have "(m*r + m)*r + m" = "m*(r^2 + r + 1)"
etc.
After month 47, you have "m*(r^47 + r^46 + ... + r^2 + r + 1)"
After month 48, you have "m*(r^48 + r^47 + ... + r^3 + r^2 + r) + 1.35*m"
After month 66, you have "m*(r^66 + r^65 + ... + r^20 + r^19 + r^18) + 1.35*m*(r^17 + r^16 + ... + r^2 + r + 1)"
We then equate this with the total pot computed earlier (1.15*(47m + 19*1.35m)). The m's cancel on both sides, and we are left with an equation in r.
This is best solved in Excel - if you're into hand calculations, use interval bisection or something starting with the interval [1, 1.15] since we know the monthly interest rate is in between those two values. The answer comes out as r = 1.00449 or thereabouts.
Then r^12 gives 1.055 or 5.5% AER.
Whether this is a good return or not is another question altogether. Considering this period spans the financial crisis, along with low interest rate period, an average return of over 5% per year tax free actually looks pretty good to me. I think I'd keep paying in to a pension with that kind of return.
Usual disclaimers: All of the above may be wrong, I am not a financial adviser, etc etc.
Edited to correct a couple of numbers - specifically the assumption that 47 months were at "m" and 19 months (48-66 inclusive) were at "1.35m"
Edited by ericgreveson on Monday 6th February 19:05
Edited by ericgreveson on Monday 6th February 19:05
Edited by ericgreveson on Monday 6th February 19:07
Gassing Station | Finance | Top of Page | What's New | My Stuff