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.

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.

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 at time 0 a sum L is lent for a series of n yearly payments. The rth payment, of amount xr, is due at the end of the rth year. Let the effective annual interest rate for the rth year be ir. Give an identity which expresses L in terms of the xr and ir.
Derive an equation to find the end-of-year future sum F that is equivalent to a series of n beginning-of-year payments B at interest rate i. Then use the equation to determine the future sum F equivalent to six B payments of $100 at 8% interest.
Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: 1R1 = 0.3%, E(2r 1) = 1.3%, E(3r1) = 8.9%, E(4r1) = 9.25% Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities.
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: Annual Rate Number of Years Invested Compounded (a) Rate of Interest a. 9% 12 Annually b. 8% 7 Quarterly C. 12% 16 Semiannually % % % (b) Number of Periods 2. In a present value of an annuity of 1 table: (Round "Rate of Interest" answers to 1 decimal place, e.g. 4.5% and other answers to O decimal places, e.g 45.) Annual Number of Years Rate Invested Number of Rents Involved Frequency of Rents (a) Rate of Interest (b) Number of Periods a. 10% 28 28 Annually b. 10% 15 30 Semiannually % % 8% 7 28 Quarterly %
Complete the following using present value. Amount $6,600, Time 10 years, Rate 2%, Compounded semiannually. What is the period used? What is the rate used? What PV factor used? What is the desired end of period amount?
Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bill rates over the following three years (ie.. years 2, 3, and 4, respectively) are as follows: 181 = 4%, E(201) = 5%, E(31) = 5.50 %, E(41) = 5.85% Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. (Round your answers to 2 decimal places.) Years AGN- Current (Long-term) Rates
Attempt History Current Attempt in Progress Wildhorse Inc. is considering modernizing its production facility by investing in new equipment and selling the old equipment. The following information has been collected on this investment: Cost Old Equipment Accumulated depreciation Remaining life Current salvage value Salvage value in 8 years Annual cash operating costs $80,240 $40,300 8 years $9,920 $0 $35,100 Cost New Equipment Estimated useful life Salvage value in 8 years Annual cash operating costs $38,000 8 years $4,800 $29,900 Depreciation is $10,030 per year for the old equipment. The straight-line depreciation method would be used for the new equipment over an eight-year period with salvage value of $4,800.
The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(rt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?
If you earn interest at percentage rate r per year and compound your interest n times per year, then in y years, $1 will grow to (1 + (r/n))ny dollars. Assuming a 10 percent annual interest rate, create a table showing the factor by which $1 will grow in 5-15 years for daily, monthly, quarterly, and semiannual compounding.
For each of the following cases, indicate (a) what interest rate columns and (b) what number of periods you would refer to in looking up the future value factor. (1) In Table 1 (future value of 1): Number of Annual Rate Years Invested Compounded Case A 5% 5 Annually Case B 8% 6 Semiannually Case A Case B . (a) % % (2) In Table 2 (future value of an annuity of 1): Annual Rate Number of Years Invested Compounded Case A 6% 9 Annually Case B 8% 5 Semiannually Case A Case B (b) periods periods (a) (b) % periods % periods
if an investment pays interest at a rate of 8% compounded semi annually, then an investment of $1000 for 3 years would be found in a table using the future value of 1 table for a. 3 periods at 8% b. 8 periods at 3% c. 12 periods at 2 % d. 6 periods at 4%
Assume a problem statement involves only single amounts, that is, no series or gradients, and the interest rate is stated as 12% per year compounded quarterly. For the following n values, determine the proper interest rate to use in the factor equations: (a) n = 20 quarters; (b) n = 10 semiannual periods; (c) n = 5 years.

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