A state's lottery winner is promised $200,000 a year for 3 years(starting at the end of the first year). Interes rate is annually 7 percent on its fund.

How much is the present value of this lottery?

Year 1 = 200,000 plus .07% = 14,000

Year 2 = 400,000 plus .07% = 28,000

Year 3 = 600,000 plus .07% = 42,000

When you say "the present value of this lottery" do you mean at the end of the 3rd year? If you mean NOW and he hasn't collected any money = 0!

Sra

What is the expected return on a portfolio consisting of an equal amount invested in each stock?

Stock Expected return
A 15%
B 10
C 22
D 14

b. What is the expected return on the portfolio if 50 percent of the funds are invested in stock C, 30 percent in stock A, and 20 percent in stock D?

To find the present value of the lottery winnings, we need to discount the future cash flows back to the present using the interest rate.

We can use the formula for the present value of an annuity to calculate this.

The formula for the present value of an annuity is:

PV = PMT * (1 - (1 + r)^-n) / r

Where:
PV = Present Value
PMT = Periodic payment
r = Interest rate per period
n = Number of periods

In this case, the periodic payment (PMT) is $200,000, the interest rate (r) is 7% or 0.07, and the number of periods (n) is 3.

Let's plug these values into the formula:

PV = 200,000 * (1 - (1 + 0.07)^-3) / 0.07

PV = 200,000 * (1 - 1.225) / 0.07

PV = 200,000 * (-0.225) / 0.07

PV ≈ - $645,714.29

The present value of the lottery winnings is approximately -$645,714.29. This negative value indicates that the lottery winner is actually receiving more than the present value of $645,714.29 over the three years, considering the interest earned on the funds.

To calculate the present value of the lottery winnings, we need to discount each future payment back to the present value.

The formula to calculate the present value of an annuity is:

PV = C / (1 + r)^n

Where:
PV = Present value
C = Cash flow per period
r = Interest rate per period
n = Number of periods

In this case, the cash flow per period is $200,000, the interest rate is 7% (or 0.07 in decimal form), and the number of periods is 3.

Let's calculate the present value:

PV = $200,000 / (1 + 0.07)^1 + $200,000 / (1 + 0.07)^2 + $200,000 / (1 + 0.07)^3

Now, let's solve this equation step by step:

PV = $200,000 / 1.07^1 + $200,000 / 1.07^2 + $200,000 / 1.07^3

PV = $200,000 / 1.07 + $200,000 / (1.07)^2 + $200,000 / (1.07)^3

PV = $186,915.89 + $174,863.39 + $163,851.86

PV = $525,631.14

Therefore, the present value of this lottery is approximately $525,631.14.