You won a lottery which pays $10,000 per year for 10 years (at the end of each year). Assuming a discount rate of 8% calculate the present value of your expected winnings.
To calculate the present value of your expected winnings, you need to discount each payment back to the present time using the discount rate of 8%. The formula to calculate the present value (PV) of a future cash flow is:
PV = CF / (1 + r)^n
where:
PV = Present value
CF = Cash flow in a specific year
r = Discount rate
n = Number of years
In this case, the cash flow is $10,000 per year for 10 years, and the discount rate is 8%. Applying the formula, you can calculate the present value as follows:
1. Calculate the present value for each cash flow:
PV1 = $10,000 / (1 + 0.08)^1 = $9,259.26
PV2 = $10,000 / (1 + 0.08)^2 = $8,564.81
PV3 = $10,000 / (1 + 0.08)^3 = $7,924.23
...
PV10 = $10,000 / (1 + 0.08)^10 = $4,317.19
2. Sum up all the present values to get the total present value of your expected winnings:
Total PV = PV1 + PV2 + PV3 + ... + PV10
Total PV = $9,259.26 + $8,564.81 + $7,924.23 + ... + $4,317.19