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Assume δt = t/(1 + t2), t > 0, where t is in years.

An investment was worth $100 at t = 2.


• (a) What will the investment be worth at t = 5? (Answer: $228.04)


• (b) What is the equivalent effective annual discount rate over the interval 2 < t < 5? (Answer: 24.03%)

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Reid Wolff
Reid WolffLv2
17 Dec 2022
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You have just won the lottery and you can choose between thefollowing payout options. The annual interest rate (EAR) is 10%. a)$100,000 right now and $60,000 every two years starting 3 yearsfrom now and ending 17 years from now (i.e., payments are at t = 0,t = 3, t = 5, … , t = 15, t = 17). b) $60,000 a year for 25 yearswith the first payment one year from today (i.e., payments are at t= 1, 2, … 24, 25). c) 25 annual payments of $45,000 and a 26thpayment of $299,000. The first payment is made right now, and the$299,000 payment is made one year after the last $45,000 payment.How much more is the best option worth today relative to the worstoption?

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