QTM 7 - Financial Maths - Tutorial Solutions

QTM 7 - Financial Maths - Tutorial Solutions - QTM Lecture...

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QTM Lecture 7 Financial Mathematics Tutorial Solutions Q1. You have just starting working at a company of financial advisors specialising in investment portfolio management for high net worth individuals. Your manager has asked you to calculate the future value of several potential investment opportunities for your clients: a) £50,000 invested in a fixed rate bond for 3 years. The fixed rate is 5% per annum. b) £100,000 invested in a fixed rate bond for 5 years. The fixed rate is 4.5% per annum. c) £250,000 invested in a fixed rate bond for 1 year. The fixed rate is 6% per annum. d) £500,000 invested in M&S fixed-rate savings for 3 years. The fixed rate is 3.25% per annum. e) £300,000 invested in a Santander fixed-rate savings scheme for 2 years. The fixed rate is 2.75% per annum. Solutions Using V = P(1 + r) n a) V = 50,000(1.05) 3 = £57,881.3 b) V = 100,000(1.045) 5 = £124,618.2 c) V = 250,000 x 1.06 = £265,000 d) V = 500,000(1.0325) 3 = £550,351.5 e) V = 300,000(1.0275) 2 = £316,726.9 Q2. Liverpool Mercantile is offering four types of fixed rate bond. A wealthy investor is trying to decide which of the four alternatives will give her the best return on her money. The four fixed-rate bonds on offer are as follows: 3 year fixed rate bond: 5% per annum 3 year fixed rate bond: 2.4% per half year 3 year fixed rate bond: 1.2% per quarter 3 year fixed rate bond: 0.41% per month
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a) Calculate the return for an investment of £150,000 on each of the above four bonds. b) Which bond would you recommend to the investor? Solutions Using V = P(1 + r) n a) i) V = 150,000(1.05) 3 = £173,643.8 ii) V = 150,000(1.024) 6 = £172,938.2 iii) V = 150,000(1.012) 12 = £173,084.2 iv) V = 150,000(1.0041) 36 = £173,804.9 b) The fourth fixed rate offer, at 0.41% per month, produces the highest return. Q3. A graduate analyst at Taylor Barrett Homes has been asked to estimate the annual increase in house prices for 2012. The graduate has found house price information from three separate sources as follows: The Royal Institute of Chartered Surveyors (RICS) stated that house prices grew by 1% in both the first and second halves of 2012. The Nationwide house price survey stated that house prices grew by 0.6% in each quarter in 2012. The Halifax monthly trends survey stated that house prices grew by 0.2% per month in 2012. a) Calculate the equivalent annual rate of growth from each of the three sources above. b) What is the average annual rate of growth from the three surveys? Solutions a) i) 1.01 x 1.01 = (1.01) 2 = 1.0201 which equates to an annual growth rate of 2.01% ii) (1.006) 4 = 1.0242 which equates to an annual growth rate of 2.42%
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iii) (1.002) 12 = 1.0243 which equates to an annual growth rate of 2.43% b) The average is a 2.29% annual rate of growth. Q4. Harburton’s Bakery has made significant investments in its main Lancashire factory over the last two years. However, the Head of Finance is concerned that interest payments, on the money borrowed for investment, are too high. He is looking to switch the debt to one of two banks, Nat West and Barclays, in order to save money. The two banks have made the following offers on the transferred debt.
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