“…When evaluating this annuity, the cash flows involved are exactly the same as the immediate annuity purchased at age 65 (scenario a); however the perceived value may be different because the decision is made at an earlier age. If an individual decides to convert the lump sum A into an annuity at retirement, the overall perceived value of this investment for the individual is: To determine whether an actuarially fairly priced annuity is attractive to purchase, we follow Hu and Scott (2007) to use the ‘relative difference between reservation price and fair price’, R , as the benchmark measure: The ‘reservation price’, also called the ‘maximum acceptable price’, is the annuity price that would make an individual indifferent to buying an annuity. According to the valuation functions above, the reservation price is the initial price, A , that makes the hyperbolic present value of an annuity, V , equal to zero.…”