You have won a contest that will pay you $10,000 a year at the end of each of the next 5 years. Based on a discount rate of 8% per year, what is the annuity worth to you today
To determine the present value of the annuity, we need to calculate the discounted value of each cash flow and sum them up. The present value formula for an annuity can be used for this calculation:
PV = C × [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value
C = Cash flow per period
r = Discount rate per period
n = Number of periods
In this case:
C = $10,000
r = 8% = 0.08 (as a decimal)
n = 5
Substituting these values into the formula, we get:
PV = $10,000 × [(1 - (1 + 0.08)^-5) / 0.08]
Let's calculate this:
PV = $10,000 × [(1 - (1.08)^-5) / 0.08]
PV = $10,000 × [(1 - 0.680583) / 0.08]
PV = $10,000 × [0.319417 / 0.08]
PV = $10,000 × 3.99271
PV = $39,927.10
Therefore, the present value of the annuity is $39,927.10.