Rita Gonzales won the $62 million lottery. She is to receive $2.8 million a year for the next 20 years plus an additional lump sum payment of $6 million after 20 years. The discount rate is 14 percent.
What is the current value of her winnings?
Well, that's a lot of money! Let's do some clown math, shall we?
First, let's calculate the current value of Rita Gonzales' yearly payments. She's getting $2.8 million every year for the next 20 years. To calculate the current value, we need to discount this amount at a rate of 14 percent.
Using my clown calculator, I'll give you the current value of those payments.
PV = $2.8 million * (1 - (1 + 0.14)^-20) / 0.14
PV = $30,628,410.89
So, the current value of Rita Gonzales' yearly payments is approximately $30,628,410.89.
Now, let's calculate the current value of the lump sum payment she will receive after 20 years, which is $6 million. We don't need to discount this amount since she will receive it in the future.
Therefore, the total current value of her winnings is approximately $30,628,410.89 (the value of the yearly payments) plus $6 million (the lump sum payment).
Adding them together, we have:
Total current value = $30,628,410.89 + $6,000,000
Total current value = $36,628,410.89
So, the current value of Rita Gonzales' winnings is approximately $36,628,410.89.
To calculate the current value of Rita Gonzales' winnings, we need to find the present value of the annual payments for the next 20 years and the present value of the lump sum payment after 20 years.
To find the present value of the annual payments, we can use the formula for the present value of an ordinary annuity:
PV = Payment × [1 - (1 + r)^(-n)] / r
Where:
PV = Present value
Payment = Annual payment
r = Discount rate
n = Number of years
In this case, the annual payment is $2.8 million, the discount rate is 14%, and the number of years is 20.
Using these values, we can calculate the present value of the annual payments:
PV_annual = $2.8 million × [1 - (1 + 0.14)^(-20)] / 0.14
Next, we need to find the present value of the lump sum payment after 20 years. This can be calculated using the formula for the present value of a future lump sum:
PV_lump_sum = Lump sum payment / (1 + r)^n
In this case, the lump sum payment is $6 million, the discount rate is 14%, and the number of years is 20.
Using these values, we can calculate the present value of the lump sum payment:
PV_lump_sum = $6 million / (1 + 0.14)^20
Now, we can calculate the total present value of Rita Gonzales' winnings by adding the present value of the annual payments and the present value of the lump sum payment.
Total Present Value = PV_annual + PV_lump_sum
Calculating this, we get:
PV_annual = $2.8 million × [1 - (1 + 0.14)^(-20)] / 0.14
PV_lump_sum = $6 million / (1 + 0.14)^20
Total Present Value = PV_annual + PV_lump_sum
To calculate the current value of Rita Gonzales' winnings, we need to find the present value of the annual payments and the lump sum payment after 20 years. We will discount these future cash flows back to the present using the discount rate of 14 percent.
1. Calculate the present value of the annual payments:
We can use the formula for the present value of an annuity to calculate the present value of the $2.8 million annual payments for 20 years. The formula is:
PV = C * [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value
C = Cash Flow per Period
r = Discount Rate
n = Number of Periods
Using the given values:
C = $2.8 million
r = 14% (0.14 as a decimal)
n = 20 years
Plug in the values and calculate the present value of the annual payments:
PV_annuity = $2.8 million * [(1 - (1 + 0.14)^-20) / 0.14]
2. Calculate the present value of the lump sum payment:
We need to calculate the present value of the $6 million lump sum payment after 20 years. Since this is a single cash flow, we can use the formula for the present value of a single amount:
PV_lump sum = Future Value / (1 + r)^n
Using the given values:
Future Value = $6 million
r = 14% (0.14 as a decimal)
n = 20 years
Plug in the values and calculate the present value of the lump sum payment:
PV_lump sum = $6 million / (1 + 0.14)^20
3. Calculate the current value:
The current value of Rita Gonzales' winnings is the sum of the present value of the annual payments and the present value of the lump sum payment:
Current Value = PV_annuity + PV_lump sum
Plug in the calculated present values and calculate the current value:
Current Value = PV_annuity + PV_lump sum
That will give you the current value of Rita Gonzales' winnings.