(Actuarial Finance problem) Assuming that \lambda=0, m=86.34, and b=9.5 as GoMa parameters, compute the value and the duration of a deferred pension annuity purchased at age 62, under a valuation rate of r=5.5%, that pays $10,000 per year for life starting at age 72. Also, compute the value and the duration for a $C per year lifetime immediate pension annuity that is purchased at age 72 under the same r=5.5% valuation rate. What value C allows a long position in the deferred annuity to exactly offset a short position in the immediate annuity for small changes in the valuation rate?