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TVM question

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?

Comments

  • 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.

  • everythingshipeverythingship Pre-CFA Posts: 2 Associate
    edited October 9

    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?

  • 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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