3. Theory of Interest - Exercise Solutions.pdf - THE CHINESE UNIVERSITY OF HONG KONG Department of Statistics RMSC2001 Introduction to Risk Management 3

3. Theory of Interest - Exercise Solutions.pdf - THE...

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THE CHINESE UNIVERSITY OF HONG KONG Department of Statistics RMSC2001: Introduction to Risk Management 3. Theory of Interest - Exercise Solutions 1. From the question it is clear that the time value of money is given by annual compounding with i c = 0 . 09. The payments made are $100, not $1. We are asked to find its present value (PV) future value at the end of the investment period (5 years) - the AV. The appropriate formula (for annual payments of $1) as given in the notes is AV = 1 i c [(1 + i c ) n - 1] = 5 . 98471061 which means the AV is $598.47. The formula for PV is (again, for annual payments of $1) PV = 1 i c 1 - 1 (1 + i c ) n = 3 . 88965126335 which means the PV is $388.97. 2. We are asked to find the AV and PV of an annuity-immediate with quarterly nominal interest of 8% and investment period 10 years, payments of $100. Use the formulae given in notes and calculate: AV = 1 i m [(1 + i m /m ) nm - 1] = 15 . 1004957952 PV = 1 i m 1 - 1 (1 + i m /m ) nm = 6 . 83886981018 These calculations assume a payment of $1 /m = $0.25 per quarter, when in fact the annuity pays $100 per quarter. We must multiply the above calculations by 100 / 0 . 25 = 400 to find the AV is $6040.20 and the PV is $2735.55. 3. The structure of the man’s savings plan is equivalent to an annuity-immediate: deposit cash at the end of each year. He wants the final value to be at least $100,000; that is, he wants the AV to be at least $100,000.
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