Consider the following spot interest rates for maturities of one, two, three, and four years. r1 = 3.7% r4 = 5.7% r₂ = 4.2% r3 = 4.9% What are the following forward rates, where fi, k refers to a forward rate for the period beginning in one year and extending for kyears? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Consider the following spot interest rates for maturities of one, two, three, and four years. r1 = 3.7% r4 = 5.7% r₂ = 4.2% r3 = 4.9% What are the following forward rates, where fi, k refers to a forward rate for the period beginning in one year and extending for kyears? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Assume that you must estimate what the future value will be two years from today using the future value of 1 table. (PV of $1, EV of $1. PVA of $1, and FVA of $1) Which interest rate column and number-of-periods row do you use when working with the following rates? (Round percentage answers to 2 decimal places.) Answer is complete but not entirely correct. Number of Periods 1. 12% annual rate, compounded annually 2.8% annual rate, compounded semiannually 3. 12% annual rate, compounded quarterly 4. 12% annual rate, compounded monthly Interest Rate 12.00 2.00 3.00 1.00 % % % % 2 80 24
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 :
consider the following spot interest rates for maturities of one, two, three, and four years. r1=4.1%, r2=4.5% r3=5.2% r=6.0% what are teh following forward rates, where fk.1 refers toa forward rate beginning in the k years and extending for the 1 year?
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 = ?
Given an interest rate of 4.8 percent per year, what is the value at date t = 10 of a perpetual stream of $3,200 payments that begins at date t = 20? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
The n-year spot rate of interest, in, can be represented by: = 0.08 0.06 x exp(-0.1n) - Calculate, to 4 decimal places (in percentages), the 3-year forward rate at time 3, f 3,3-
Suppose we observe the following rates: 1R1 = 10%, 1R2 = 12%. If the unbiased expectations theory of the term structure of interest rates holds, what is the 1-year interest rate expected one year from now, E(2r1)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
a. If the one-year discount factor is 0.9217, what is the one-year interest rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) b. If the two-year interest rate is 8.5%, what is the two-year discount factor? (Do not round intermediate calculations. Round your answer to 4 decimal places.) c. Given these one- and two-year discount factors, calculate the two-year annuity factor. (Do not round intermediate calculations. Round your answer to 4 decimal places.) d. If the PV of $10 a year for three years is $25.54, what is the three-year annuity factor? (Do not round intermediate calculations. Round your answer to 4 decimal places.) e. From your answers to (c) and (d), calculate the three-year discount factor. (Do not round intermediate calculations. Round your answer to 4 decimal places.) a. Interest rate % b. Discount factor c. Annuity factor d. Annuity factor e. Discount factor
For each of the following cases, indicate (a) to what interest rate columns and (b) to what number of periods you would refer in looking up the future value factor. (Round percentages to 2 decimal places, e.g. 5,275.)(1) In Table 1 (future value of 1): Annual Rate Number ofYears Invested Compounded Case A 4% 3 Annually Case B 9% 5 Semiannually (a) (b) Case A % periods Case B % periods (2) In Table 2 (future value of an annuity of 1): Annual Rate Number ofYears Invested Compounded Case A 6% 5 Annually Case B 12% 6 Semiannually (a) (b) Case A % periods Case B % periods
Given an interest rate of 5.7 percent per year, what is the value at t = 8 of a perpetual stream of $4,100 annual payments that begins at t = 18? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value at t = 8 $
For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor. 1. In a future value of 1 table: a. b. J C. a. b. Annual Rate C. 10% 8% 10% Annual Rate 9% 11% Number of Years Invested 12% 2. In a present value of an annuity of 1 table: (Round answers to 1 decimal place, e.g. 458,58.1.) Number of Rents Involved Number of Years Invested 29 16 10 7 7 20 29 32 Compounded 28 Annually Quarterly Semiannually Frequency of Rents Annually Semiannually (a) Rate of Interest Quarterly (a) Rate of Interest % % % % % % (b) Number of Periods (b) Number of Periods
The n-year spot rate of interest per annum, in, is given by: b in = a(1.1)" +- n for n = 1, 2 and 3 and where a and b are constants. With time measured in years from the present, the implied one-year forward rates applicable at time 0 and at time 1 are 7.3% and 6.8%, respectively. Showing all of your workout, calculate to 5 decimal places the following: (i) the values of a and b; (ii) the implied two-year forward rate applicable at time 1; (iii) the price per £1 nominal at time t = 0 of a bond which pays annual coupons of 7% in arrears and is redeemed at 95% after 3 years.

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