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Up11
I just want to know if my thought process is correct. I want to know “how much to save”.
Lets say:
Rate of return = 10%
Life expectancy = 90
Retirement age = 60
Current age = 25
Monthly income = $4000
Saving frequency is weekly
Compounded semi-annually
End of period CF and retirement happens on first day of retirement
I would find the periodic rate since it’s compounded semi-annually.
periodic rate = (1 + 10% / 2) ^ (2 / 12) – 1
Then use it to find the PV of how much I would need if from 60 to 90.
r = 0.816% n = (90-60) * 12 PMT = $4000 So the PV = $1,247,329.99
So this is how much I would need when I retire, so now I need to know how much to save.
Since Im saving weekly (52) I would need PMT
r = 0.0816 n= (60-25) * 52 FV = $1,247,329.99 PV=0
PMT = 298.23/week
Conversely, if wanted to find out what the monthly retirement income would be if I saved quarterly instead would the calculations be similar?
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Up4
My calculation has a slight difference in FV due to more decimal points in i/y (usually I go for 4 dp): n=140, i/y = 2.4695, PV=0, PMT = -2000, FV = 2,383,163.16 (at t=60)
Here we expect the FV to be significantly higher vs. the first very first question, given the higher savings per period ($2,000 per quarter vs. $29.6 per week which is roughly equal to $384.80 per quarter). So the FV here is about $2.38million when you save more ($2,000 per quarter) although the compounding period is less ($29.6 per week), given the same annual effective rate.
So next we want to find the monthly annuity income from the pot of money at retirement age (t=60), so PV should be the pot of money $2.38m:
Then, at t=60, PV = – 2,383,163.16, N = 360, I/Y = 0.816, Monthly PMT = 20,548.59
Yes seems quite high, but there is the power of monthly compounding on such a large $2.38m base over 30 years.
Hope I’ve done this right, have a check?
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Up3
You are correct.
Could you also double check if this is right for me please?
Saving $2000 quarterly with semi-annual compounding from 25 to 60
periodic rate = (1 + 10% / 2) ^ (2 / 4) – 1 = 0.0246
Find FV at retirement age
n = 140 i = 2.46 pv = 0 pmt = -2000 FV = 2,360,465.53
Finding monthly income from 60 to 90
Periodic rate = 0.816
FV = 2,360,465.53 N = 360 I = 0.816 Monthly pmt = 30,650.27
Seems quite high, is this correct?
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Up0
Agree with the monthly periodic rate.
However in your first TVM calculation, I seem to get a PV of $463,908 with the same input of: r = 0.816 n = (90-60) * 12 PMT = $4000.
In the second TVM calcs for weekly savings: I thought 0.1878% should be the weekly periodic rate, instead of the monthly rate of 0.816%. PMT seems to be $29.6 per week savings assuming my previous PV above of $463,908 is correct. Can you double check?
The calculation should be similar if you change savings frequency, but you need to update the periodic rate accordingly.
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Up0
It may seem to be extremely high, the power of monthly compounding on such a massive foundation of $2.38 million over the course of thirty years is significant.
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