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Answer these questions in a 1 to 2-page paper. Please use appropriate citations throughout your paper.
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.
Calculate the present value of the payments you will receive. Show your calculations using formulas in your paper or in an attached spreadsheet file.
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.
Instructions
Answer these questions in a 1 to 2-page paper.
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.
One way to solve the assignment problem
1A. Calculate the present value of the payments you will receive.
Show your calculations
using formulas in your paper or in an attached spreadsheet file.
Strayer Lottery Jackpot = $11,000,000
Number of installments (N) = 26
Lottery paid in 26 months = 11,000,000/26 = 423,076.92
Quoted annual interest rate= 9%
Monthly interest rate = 9/12 = 0.75%
Calculating for the effective annual rate (EAR):
Formula for: Effective % Rate
EFF% = (1+(INOM/M))m – 1 EFF% = (1+(INOM/M))m – 1 = (1 + (0.0075))12 – 1
= (1.0075)12 – 1 (Note input1.0075 press^ for the 12th power then press12 on
calculator to get 1.0938)
= 1.0938 – 1
= 0.0938 or 9.38%
The Present Value
Lottery paid in 26 months = 11,000,000/26 = 423,076.92
Formula for: PV= (Rate, nper, pmt, fv, type)
PV=rate*nper*pmt*fv*type
Rate= 0.093807 or 9.3807%
Number of installments (N) = 26
PMT= 423,076.92
FV=0
Type=1
PV=rate*nper*pmt*fv*type
PV= (0.093807, 26, 423076.92, 0, 1)
Answer: Present Value (PV) = $4,453,789.94 Payments you will receive
END.
NOTE/ EXPLANATION FOR SET UP:
Calculating the Present Value of annual installments is a multistep process, first requiring we take the provided information and compute the monetary value of the 26 installments and monthly interest to find the Effective Annual Rate (EAR). The jackpot total of $11,000,000 divided by 26 installments totals $423,076.92, the annual interest rate is 9%, and the monthly compounding interest rate is 0.75% (9/12). The EAR formula is EFF% = {1+(INOM/M)}m-1, or {1+ Nominal rate (0.0075)}^ months (12) -1; this calculates to (1.0075)^12 – 1, and 1.093807 – 1= 0.093807. The Effective Annual Rate is 9.3807%
Arriving at the Present Value of annual installment payments requires another formula, leveraging the previous calculations of $423,076.92 (11,000,000 / 26 = 423,076.923077) and 9.3807%. That formula is Present Value = Rate * Number of Periods * Payment * Future Value * Type, or PV=rate*nper*pmt*fv*type. Plugging in our values, the equation becomes PV = (0.093807) * 26 * 423,076.92 * 0 * 1.
The answer is that the Present Value is $4,453,789.94.
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