CFA CFA Level 1 TVM question

TVM question

  • This topic has 3 replies, 2 voices, and was last updated Dec-20 by rollover2.
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    • everythingship
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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 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?

    • rollover2
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      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.

    • everythingship
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      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?

    • rollover2
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      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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