# Solution for Time Value of Money

Topics: Time value of money, Time, Money / Pages: 2 (497 words) / Published: Sep 20th, 2014
FIN41340: Quantitative Methods in Finance
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?

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