Prob Set 1 Lottery question 3 3. You just won $250,000 on a lottery ticket. You...

Prob Set 1 Lottery question 3

3. You just won $250,000 on a lottery ticket. You plan to save the money in a retirement account expected to return 8% per year. If you intend to retire in 20 years, how much are these winnings expected to be worth when you retire?

a) Suppose you win the lottery but are given the following choice: 1) receive $250,000 today in a lump sum or 2) receive annual payments of $20,000 for 20 years, with the first payment of $20,000 paid immediately. If the appropriate interest rate/discount rate is 6%, which option would you choose based on which option has the greatest Net Present Value (NPV)?

b) What if the appropriate interest rate/discount rate is 4.5%, which option would you choose? Explain why.

Solutions

Expert Solution

You just won $250,000 on a lottery ticket. You plan to save the money in a retirement account expected to return 8% per year. If you intend to retire in 20 years, how much are these winnings expected to be worth when you retire?

Calculating the NPV of the annuity at the begining of the year:

As the lumpsum amount of 250000 is higher than the PV of annuity due, lumpsum is a better option.

b) What if the appropriate interest rate/discount rate is 4.5%, which option would you choose? Explain why.

Calculating the NPV of the annuity at the begining of the year:

As the lumpsum amount of 250000 is lower than the PV of annuity due, Annuity is a better option.

jeff jeffy answered 1 year ago

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