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Rita Gonzales won the $62 million lottery. She is to receive $1.9 million a year for...

Rita Gonzales won the $62 million lottery. She is to receive $1.9 million a year for the next 25 years plus an additional lump sum payment of $14.5 million after 25 years. The discount rate is 13 percent. What is the current value of her winnings? Use Appendix B and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods.(Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Expert Solution

Answer:

Person RG won a lottery $62 million. She will be paid with yearly payments. Thus, payment for one year is $1.9 million for the next 25 years. The lump sum amount of $14.5 million will be paid in year 25. The applicable discount rate is 13%.

Current value of the winnings of person RG is the present value of the payments that can be received by her in the future. Hence, sum of the present value of annuity and present value of the single payment in year 25 is the current value of the winnings.

First, calculate the present value of annuity using the following equation:

here,

Present value of annuity

Annuity amount

Interest rate/Discount rate

Number of periods

Substitute $1.9 million for annuity amount, 0.13 for discount rate, and 25 for number of periods in the equation of present value of annuity:

Therefore, the present value of annuity is $14.0630666 million.

Now, calculate the present value of the lump sum payment in last year using the present value equation:

here,

Present value

Future value

Interest rate

Number of periods

Substitute $14.5 million for future value, 0.13 for discount rate, and 25 for number of periods in the equation of present value:

hence, the present value of the lump sum payment is $0.682964 million.

Now, calculate the current value of the winnings:

Current value of winnings = PV of annuity + PV of lump sum payment

= $14.0630666 million + $0.682964 million

= $14.7460306 million

Therefore, the current value of the winnings is $14.7460306 million

jeff jeffy answered 1 year ago

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