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FIN41340: Quantitative Methods in FinanceTutorial: Time Value of MoneyLecturer:Darragh O’DowdTutorial Questions1. What is the present value of a 3-year annuity of $100 if the interest rateis 6%? What is the present value of this annuity, if you have to wait twoyears instead of one year for the first payment?2. Your hedge fund can lease a supercomputer for the purposes of high fre-quency trading for $8,000 per year (paid at year end) for six years. Al-ternatively, it can buy the computer for $40,000. The computer will bevalueless after six years. If the interest rate your company can earn on itsfunds is 7%, is it cheaper to buy or lease?3. Suppose that you receive annual payments of 10,000 per annum for aperiod of 10 years. What is the present value of this stream of paymentsif the first payment will be made in 4 years and the interest rate is 5%?4. The $40 million lottery you just won actually pays $2 million per annumfor 20 years. If the discount rate is 8% and the first payment comes in 1year, what is the present value of the winnings? What if the first payment