The force of interest 8(t) is a function of time and at any time t, measured in years, is given by the formula: 8(t) = {° (0.03 +0.005t 0.06 for 0 6 (i) (ii) Derive, and simplify as far as possible, expressions in terms of t for the accumulated amount at time t of an investment of £1 made at time t = 0. You should derive separate expressions for both sub-intervals. Using the result in part (i), calculate the value at time t = 3 of a payment of £2,000 made at time t = 7. (iii) Calculate, to the nearest 0.1%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii). (iv) A continuous payment stream, under which the rate of payment per annum at time t is p(t) = 500e-0.01t, is invested between t = 10 and t = 15. Using the result in part (i), calculate the present value (at time t = 0) of this investment.
The force of interest 8(t) is a function of time and at any time t, measured in years, is given by the formula: 8(t) = {° (0.03 +0.005t 0.06 for 0 6 (i) (ii) Derive, and simplify as far as possible, expressions in terms of t for the accumulated amount at time t of an investment of £1 made at time t = 0. You should derive separate expressions for both sub-intervals. Using the result in part (i), calculate the value at time t = 3 of a payment of £2,000 made at time t = 7. (iii) Calculate, to the nearest 0.1%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii). (iv) A continuous payment stream, under which the rate of payment per annum at time t is p(t) = 500e-0.01t, is invested between t = 10 and t = 15. Using the result in part (i), calculate the present value (at time t = 0) of this investment.
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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Jus part I) and Ii)
Transcribed Image Text:The force of interest 8(t) is a function of time and at any time t, measured in years, is given
by the formula:
8(t) = {°
(0.03 +0.005t
0.06
for
0<t≤ 6
for
t> 6
(i)
(ii)
Derive, and simplify as far as possible, expressions in terms of t for the
accumulated amount at time t of an investment of £1 made at time t = 0. You
should derive separate expressions for both sub-intervals.
Using the result in part (i), calculate the value at time t = 3 of a payment of £2,000
made at time t = 7.
(iii)
Calculate, to the nearest 0.1%, the constant nominal annual rate of interest
convertible half-yearly implied by the transaction in part (ii).
(iv) A continuous payment stream, under which the rate of payment per annum at time t
is p(t) = 500e-0.01t, is invested between t = 10 and t = 15. Using the result in
part (i), calculate the present value (at time t = 0) of this investment.
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