Mark has won a contest in which he will receive $10,000 at the end of each of the next 10 years and then $20,000 a year for the next 30 years after that. With an 8% discount rate, what is the present value of Mark's prize?
PV = 10000(1 - 1.08)^-10)/.08 + 20000(1 - 1.08^-30)/.08 (1.08)^-10
= 171391.45
or
pretend you are gettting 20,000 for 40 years - the 10,000 for the first 10 years
= 20000(1 - 1.08^-40)/.08 - 10000(1 - 1.08^-10)/.08
= 171391.45
To calculate the present value of Mark's prize, we need to find the sum of the present values of each cash flow. The formula to calculate the present value of a future cash flow is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.
In this case, Mark will receive $10,000 at the end of each of the next 10 years, and then $20,000 a year for the next 30 years. Let's calculate the present value of each cash flow separately:
For the $10,000 cash flows, we use the formula:
PV = $10,000 / (1 + 0.08)^n
Where n represents the number of years. In this case, n ranges from 1 to 10 as Mark will receive $10,000 for 10 years. Let's calculate the present value of these cash flows:
PV1 = $10,000 / (1 + 0.08)^1
PV2 = $10,000 / (1 + 0.08)^2
PV3 = $10,000 / (1 + 0.08)^3
...
PV10 = $10,000 / (1 + 0.08)^10
For the $20,000 cash flows, we use the formula:
PV = $20,000 / (1 + 0.08)^n
In this case, n ranges from 11 to 40 as Mark will receive $20,000 for 30 additional years. Let's calculate the present value of these cash flows:
PV11 = $20,000 / (1 + 0.08)^11
PV12 = $20,000 / (1 + 0.08)^12
...
PV40 = $20,000 / (1 + 0.08)^40
Finally, we add up all the present values to find the total present value of Mark's prize:
Total PV = PV1 + PV2 + ... + PV10 + PV11 + PV12 + ... + PV40
By substituting the values and performing the calculations, we can find the present value of Mark's prize.