Question

You have just won the lottery and will receive $1,500,000 in one year. You will receive payments for 30 years, and the payments will increase 2.7 percent per year.

If the appropriate discount rate is 6.8 percent, what is the present value of your winnings? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

We can use the present value of a growing annuity equation to find the value of your deposits today. Doing so, we find:

PV = C{[1 / (r – g)] – [1 / (r – g)] × [(1 + g) / (1 + r)]^t}

PV = $1,500,000{[1 / (0.068 – 0.027)] – [1/(0.068 – 0.027)] × [(1 + 0.027) / (1 + 0.068)]³⁰}

PV = $25,280,038.83