BOOK_Answers_Chpt_1_2_3_and_4_Sept_10_2007

BOOK_Answers_Chpt_1_2_3_and_4_Sept_10_2007 - CHAPTER 1...

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C HAPTER 1 ANSWERS: EXERCISE 1. With simple interest, interest is earned only on the original principal. With compound interest, interest is earned on both the original principal and interest earned so far. 2. The nominal interest rate does not include the effect of compounding. The effective interest rate already includes the effect of compounding. The nominal interest rate is equal to annual effective rate with annual compounding. 3. The formula is: 1 1 - + = c nom eff c i i where, i eff = effective annual interest rate or APR i n = nominal annual interest rate c = number of compounding periods per year WORD PROBLEM 1.1. Interest earned per year = 20,000 (0.05) = $ 1,000 Accumulated interest over 4 years = 4 (1,000) = $ 4,000 You have to pay back $ 4,000 at the end of the loan. 1.2. From June 1 st , 2003 to May 31 st , 2006, the loan is taken for 3 years. Interest earned over three years = 5,000(1.08) 3 – 5,000 = $ 1,298.56 1.3. a) 10 % (nominal rate = annual effective rate) 1
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b) ( 1+ (0.1/2)) 2 -1 = 0.1025 =10.25 % (to 2 dp) c) ( 1+ (0.1/4)) 4 – 1 = 0.1038 = 10.38 % (to 2dp) d) ( 1+ (0.1/12)) 12 – 1 = 0.1047 = 10.47 % (to 2dp) e) ( 1 + (0.1/52)) 52 – 1 = 0.1051 = 10.51 % (to 2dp) f) ( 1+ (0.1/365)) 365 – 1 = 0.1052 = 10.52 % (to 2dp) CHAPTER SPECIFIC PROBLEM On the second round of financing you should ask for about 10x the first round so 10 x 10,000 = $100,000 C HAPTER 2 Chapter 2 Answers EXERCISE 1. The decreasing purchasing power of money. 2. Consumer Price Index (CPI) 3. Inflation, f, and the uninflated real rate of return, i’. i = i’ + f + i’f or d = i + f + if (using FE convention where d is the market interest and i is the real rate of return) WORD PROBLEMS 1. d = i + f + if = 0.02 + 0.10 + (0.02)(0.10) = 0.122 P = F(1+d) -n = 15 ( 1+0.122) -2 = $ 11.92 (to 2 dp) 2. Future value = P(1+d) n a) with no inflation, d=i Future value = 7,500 (1+0.08) 8 = $ 13,881.98 (to 2 dp) b) with inflation of 3%, d = 0.03 + 0.08 + (0.03)(0.08) = 0.1124 Future value = 7,500 ( 1+0.1124) 8 = $ 17,585.27 c) The future value of $ 7,500 today is larger if we take inflation into account. Thus if future inflation rate turns out to be larger than expected, the borrowers will benefit since the 2
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amount they borrowed today, in today’s dollars, would be less than the amount they have to pay back in future, also expressed in today’s dollars. 3. d = i + f + if d –i = f(1+i) f = (d-i)/(1+i) substituting d=0.14, i=0.095, f = (0.14 – 0.095) / (1+0.095) = 0.0411 = 4.11% (to 2dp) 4. No of popcorn packets sold in the third year = 50,000 x 1.1 x 1.05 = 57,750 Price of popcorn in year 3 = 3(1.03) 2 = $ 3.18 (to 2 dp) No of limejuices bottle sold in the third year = 75,000 x 1.1 x 1.05 = 86,625 Price of limejuice in year 3 = 1.2(1.03) 2 = $ 1.27 (to 2 dp) Sales revenue in the third year = [ 57,750 x $ 3.18 ] + [ 86,625 x $ 1.27 ] = $ 293,659 (to nearest dollar) 5. Era of incremental change, since the entrepreneur is selling
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BOOK_Answers_Chpt_1_2_3_and_4_Sept_10_2007 - CHAPTER 1...

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