Question

Assume a person has the option of receiving an ordinary annually paying $50000 per year for the next 25 years at 6% discount rate or accepting a single payment of s650000. Which is the better choice?

Answer 1

To determine which option is the better choice, we can calculate the present value of the annuity payments using the formula for present value of an ordinary annuity:
PV = PMT * ((1 - (1 + r)^-n) / r)
Where:
PV = present value
PMT = annual payment ($50,000)
r = discount rate (6% or 0.06)
n = number of years (25)
PV = $50,000 * ((1 - (1 + 0.06)^-25) / 0.06)
PV = $50,000 * ((1 - (1.06)^-25) / 0.06)
PV = $50,000 * ((1 - 0.37689) / 0.06)
PV = $50,000 * (0.62311 / 0.06)
PV = $50,000 * 10.38517
PV = $519,258.50
Therefore, the present value of the annuity payments is approximately $519,258.50.
Comparing this to the single payment option of $650,000, it is clear that the single payment of $650,000 is the better choice as it offers a higher present value than the annuity payments.