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I am is faced with a choice of two alternatives. There really is no right or wrong answer, I just want to hear someone else's input/methodology. Here are the two choices:

  • Keep paying $5,722.56 for the next 70 quarters to fund a pension liability

  • or pay off the entire amount for a lump sum of $229,293.73

I am currently using a benchmark rate of 3.3% (which says I should pay the lump sum), but I believe my benchmark rate should be higher.

My question is this:

  1. I want to confirm the discount rate on how the lump sum was calculated
  2. At what discount rate would it be worth continuing to pay off the $5,722.56 per quarter?
  3. Which option would you choose: quarterly payments or lump sum? What discount rate did you use? An explanation on why you chose the interest rate would be appreciated, not required.

The 5,722.56 is paid a the end of each quarter (March 31st, June 30th, etc). The lump sum payment of $229,293.73 would be due now if I chose to do that.

  • While I have provided an answer to how you can do your computations, your question is not at all clear as to how or why the interest is being chosen. If it is a pension liability, the pension plan document would likely spell out what interest rate is to be used, and what the lump sum versus quarterly payment amounts are. – Dilip Sarwate Apr 19 '12 at 19:15
  • The pension company arrived at a 229,293.73 lump sum payment based on 70 payments of 5,722.56. I calculated their discount rate, and I want to verify it with someone else's calculation. The 3.3% interest rate is the benchmark I am using based on what I have earned for the past 2 years in an investment account. However I believe it should be higher. My questions is basically: which option would be better? Pay off $229K now or pay $5.7K for the next 70 periods? – Daniel Apr 19 '12 at 19:44
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Assuming for simplicity that the lump sum was due April 1 (start of the quarter), and payments would begin on June 30th and continue for 70 quarters, with 3.3% interest compounded quarterly (that is, 0.825% per quarter), the lump sum P corresponding to quarterly payment Q is given by

P = (Q/0.00825)*(1 - 1/(1.00825)^70) = Q*53.01439...

and so Q = 5,722.56 corresponds to a lump sum payment of $303,378.05 due on April 1. You can juggle the numbers and interest rates, add in 19 days of interest etc if you like.

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