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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 semiannually
End of period CF and retirement happens on first day of retirement
I would find the periodic rate since it’s compounded semiannually.
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 = (9060) * 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= (6025) * 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?

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 = (9060) * 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.

You are correct.
Could you also double check if this is right for me please?
Saving $2000 quarterly with semiannual 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?

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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