Lottery Jackpot and Bonds

Lottery Jackpot and Bonds

Answer these questions in a 1 to 2-page paper.

1. You have just won the Strayer Lottery jackpot of $11,000,000. You will be paid in twenty-six equal annual installments beginning immediately. If you had the money now, you could invest it in an account with a quoted annual interest rate of 9% with monthly compounding of interest.
   1. Calculate the present value of the payments you will receive. Show your calculations using formulas in your paper or in an attached spreadsheet file.
   2. Explain why there is a difference between the present value of the Strayer lottery jackpot and the future value of the twenty-six annual payments based on your calculations and the information provided.
2. Discuss the risk and return indicated by different bond ratings. Support your answer with references to your research.
   1. Use various bond websites to locate one of each of the following bond ratings: AAA, BBB, CCC, and D. Research the differences between the bond ratings, the required interest rates, and the risk. List the websites used as sources for this research.
   2. Identify the strengths and weaknesses of each rating

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APA

Lottery Jackpot and Bonds

Present Value of Strayer Lottery Jackpot

Winning the Strayer Lottery jackpot of $11,000,000 paid in twenty-six equal annual installments immediately means you will receive a set of cash flows over the next 26 years. To calculate the present value (PV) of the payments, we need to apply the formula for the present value of an annuity due, as the first payment is made immediately.

The Present Value of Annuity Due formula is:

PV=P×(1−(1+r)−nr)×(1+r)PV = P \times \left( \frac{1 – (1 + r)^{-n}}{r} \right) \times (1 + r)PV=P×(r1−(1+r)−n​)×(1+r)

Where:

• $P$ = Payment amount per period
• $r$ = Monthly interest rate
• $n$ = Total number of periods (in months)

We know:

• The total jackpot is $11,000,000.
• The annual payment is $11,000,000 ÷ 26 = $423,076.92.
• The interest rate is 9% annually or 0.75% per month (9% ÷ 12 months).
• The number of months is 26 years × 12 months = 312 months.

To calculate the present value, we first need the annual interest rate to be converted into a monthly rate, and then we plug the values into the formula.

Now, we can calculate:

PV=423,076.92×(1−(1+0.0075)−3120.0075)×(1+0.0075)PV = 423,076.92 \times \left( \frac{1 – (1 + 0.0075)^{-312}}{0.0075} \right) \times (1 + 0.0075)PV=423,076.92×(0.00751−(1+0.0075)−312​)×(1+0.0075)

Performing the math:

$$PV=423,076.92\times 121.0083\times 1.0075=51,288,688.85$$

Thus, the present value of the payments is approximately $51,288,688.85.

Difference Between Present Value and Future Value

The future value (FV) of the 26 payments would be…