Maturity (years) Zero-coupon YTM= 1 4.00% 2 5.50% 3 5.50% 4 5.00% The rate for an investment that begins in one year and matures in five years would be%. (Round the final answer two decimal places. Round all intermediate values to four decimal places as needed.) 5 4.50% Suppose you wanted to lock in an interest rate for an investment that begins in one year and matures in five years. What rate would you obtain if there were no arbitrage opportunities?
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- Refer to the following table. Maturity (years) Zero-coupon YTM=r Suppose you wanted to lock in an interest rate for an investment that begins in one year and matures in five years. What rate would you obtain if there were no arbitrage opportunities? 1 3.96% The rate for an investment that begins in one year and matures in five years would be. (Round the final answer two decimal places. Round all intermediate values to four decimal places as needed.) K 2 5.73% 3 5.73% 4 5.21% 5 4.68%Suppose the term structure of risk-free interest rates is as shown below: Term Rate (EAR %) 1 year 1.98 2 years 2.35 3 years 2.63 5 years 3.23 ← 7 years 3.84 10 years 4.13 20 years 4.99 a. Calculate the present value of an investment that pays $5,000 in two years and $2,000 in five years for certain. b. Calculate the present value of receiving $400 per year, with certainty, at the end of the next five years. To find the rates for the missing years in the table, linearly interpolate between the years for which you do know the rates. (For example, the rate in year four would be the average rate in year three and year five) c. Calculate the present value of receiving $2,300 per year, with certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. (Hint: Use a spreadsheet.) a. Calculate the present value of an investment that pays $5,000 in two years and $2,000 in five years for certain. The present value of the investment is $. (Round to the nearest…Consider the following spot interest rates for maturities of one, two, three, and four years. r1 = 6.10% r2 = 6.00% r3 = 5.80% r4 = 5.50% What are the following forward rates? Hint: f1, k refers to a forward rate for the period beginning in one year and extending for k years. fk,1 refers to a forward rate beginning in k years and extending for 1 year. f1,1 : f1,2 : f1,3 : f2,1: f3,1 :
- Suppose the term structure of risk-free interest rates is as shown below. 1 yr Term 2 yr 3 yr 5 yr 7 yr 10 yr 20 yr Rate (EAR %) 2.08 2.42 2.61 3.24 3.87 4.04 5.07 a. Calculate the present value of an investment that pays $5,000 in two years and $3,000 in five years for certain. b. Calculate the present value of receiving $300 per year, with certainty, at the end of the next five years. To find the rates for the missing years in the table, linearly interpolate between the years for which you do know the rates. (For example, the rate in year 4 would be the average rate in year 3 and year 5.) c. Calculate the present value of receiving $2,300 per year, with certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. (Hint: Use a spreadsheet.) a. Calculate the present value of an investment that pays $5,000 in two years and $3,000 in five years for certain, The present value of the investment is $ (Round to the nearest dollar.)Suppose the term structure of risk-free interest rates is as shown below: 5 yr 7 yr 10 yr 20 yr Term 1 уг 2 yr 3 yr 3.24 3.79 4.09 5.05 2.07 2.46 2.71 Rate (EAR %) a. Calculate the present value of an investment that pays $1,000 in two years and $3,000 in five years for certain. b. Calculate the present value of receiving $100 per year, with certainty, at the end of the next five years. To find the rates for the missing years in the table, linearly interpolate between the years for which you do know the rates. (For example, the rate in year 4 would be the average rate in year 3 and year 5.) c. Calculate the present value of receiving $1,800 per year, with certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. (Hint: Use a spreadsheet.)1. How much would you have at the end of five years if you invested P50,00Q at 10.5% interest rate? a) P63,814.08 b) P82,372.34 c) P142,650.71 2. Discounting basically looks for which type of value? a) Present Value b) Future Value 3. The risk return trade-off can be summed up by which phrase? a) Time is gold b) No pain, No Gain c) A penny saved is a penny earned. 4. Check if your answer is correct by calculating the FV of your answers in Item 2 and the interest earned. a) FV P1,000,000; Interest P393,000.11 b) FV P1,000,000; Interest P390,000.11 c) FV P1,000,000; Interest P394,000.11 5. If you want to have a million pesos in five years, how much should you deposit/invest right now at a 10.5% interest rate? a) P350,506.50 b) P783,526.17 c) P606,999.89
- Suppose that the current one-year zero-coupon rate is 2.5% and that the expected one-year rate during each of the subsequent four years is 2.0%, 2.5%, 3.0%, and 3.5%. Under the expectations theory, what is the current 5-year zero-coupon interest rate? Enter the answer in percentage points; for example, if the answer is 5.25%, enter 5.25 rather than .0525.Question 2. Suppose the current ZCB prices for maturity in two years and in five years are 0.8 and 0.7, respectively. Suppose the two-year forward three-year libor rate is 4%. Determine if there is an arbitrage opportunity. If so, find an arbitrage portfolio. Make sure that you verify the portfolio is an arbitrage portfolio. Hint: In your arbitrage portfolio you will need to include a forward rate agreement.Refer to the following table: (Click on the following icon in order to copy its contents into a spreadsheet.) Maturity (years) 1 2 3 4 5 Zero- coupon YTM 4.00% 5.50% 5.50% 5.00% 4.50% What is the forward rate for year 2 the forward rate quoted today for an investment that begins in one year and matures in two years)? Note: Use at least four decimal places in all intermediate calculations. Question content area bottom Part 1 The forward rate for year 2 is enter your response here %. (Round to two decimal places.)
- Consider the following spot interest rates for maturities of one, two, three, and four years. r₁ = 4.3% 2 = 4.9% √3 = 5.6% r4 = 6.4% What are the following forward rates, where fkn refers to a forward rate beginning in k year(s) and extending for n year(s)? f2,1 = ? f3,1 = ? f2,2 = ?The pure expectations theory, or the expectations hypothesis, asserts that long-term interest rates can be used to estimate future short-term interest rates. Based on the pure expectations theory, is the following statement true or false? Q1. A certificate of deposit (CD) for two years will have the same yield as a CD for one year followed by an investment in another one-year CD after one year. a. True b. False Q2. The yield on a one-year Treasury security is 4.9200%, and the two-year Treasury security has a 5.9040% yield. Assuming that the pure expectations theory is correct, what is the market’s estimate of the one-year Treasury rate one year from now? (Note: Do not round your intermediate calculations.) a. 5.8627% b. 6.8973% c. 7.8629% d. 8.7596% Q3. Recall that on a one-year Treasury security the yield is 4.9200% and 5.9040% on a two-year Treasury security. Suppose the one-year security does not have a maturity risk premium, but the two-year security does and it is 0.2%. What is…Suppose the term structure of risk-free interest rates is as shown below: 5 yr 7 yr 10 yr 20 yr Term 1 yr 2 yr 3 yr 2.42 2.77 3.31 3.75 4.15 4.93 1.98 Rate (EAR %) What is the present value of an investment that pays $103 at the end of each of years 1, 2, and 3? If you wanted to value this investment correctly using the annuity formula, what discount rate should you use? What is the present value of an investment that pays $103 at the end of each of years 1, 2, and 3? The present value of the investment is $294.08. (Round to the nearest cent.) If you wanted to value this investment correctly using the annuity formula, what discount rate should you use? The discount rate you should use if you want to use the annuity formula is 2.94%. (Round to two decimal places.)