# Solution for Time Value of Money

Tutorial: Time Value of Money

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Dr. Thomas Conlon conlon.thomas@ucd.ie Tutorial Questions

1. What is the present value of a 3-year annuity of $100 if the interest rate is 6%? What is the present value of this annuity, if you have to wait two years instead of one year for the ﬁrst payment?

2. Your hedge fund can lease a supercomputer for the purposes of high frequency trading for $8, 000 per year (paid at year end) for six years. Alternatively, it can buy the computer for $40, 000. The computer will be valueless after six years. If the interest rate your company can earn on its funds is 7%, is it cheaper to buy or lease?

3. Suppose that you receive annual payments of 10, 000 per annum for a period of 10 years. What is the present value of this stream of payments if 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 annum for 20 years. If the discount rate is 8% and the ﬁrst payment comes in 1 year, what is the present value of the winnings? What if the ﬁrst payment comes immediately?

5. How much must be saved annually, beginning 1 year from now, in order to accumulate $50, 000 over the next 10 years, earning 9% annually?

Tutorial Answers

1. The present value is $252.17.

2. The present value of $38, 132.32 is less than 40, 000, so it is cheaper to lease the supercomputer than to buy it.

3.

P V0 = $66, 703.25

4. The present value is $21.21 million.

5. $3, 291.88

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Self Study Questions

1. Your car loan requires payments of $200 per month for the ﬁrst year and payments of $400 per month during the second year. The annual interest rate is 12% and payments begin in one month. What is the present value of this 2-year loan?

2. A perpetuity of $5, 000 per year beginning today is said to oﬀer a 15% interest rate. What is its present value?

3. Starting on her 35th birthday, a woman