The force of interest 8(t) is a function of time and at any time t, measured in years, is given by the formula: s(t) = {0.03 (0.03 +0.005t for 0.06 for 0 6 (i) 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. (ii) 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: s(t) = {0.03 (0.03 +0.005t for 0.06 for 0 6 (i) 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. (ii) 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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SOLVE ONLY PARTS III) AND IV), USING FORMULAS, NO TABLES, CORRECT ANSWERS ARE FOR PART III) i^2 = 5.5% pa AND FOR PART IV) PV = £1,146.13, GIVEN THAT ANSWERS FOR PART I) IS A(T) = EXP(0.03T + 0.0025T^2) FOR 0 < T < 6 AND A(T) = EXP(-0.09 + 0.06T) FOR 6 < T AND FOR PART II) IS C3 = £2000 X (EXP(0.1125)) / (EXP(0.33)) = £1,609.05
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:
s(t) = {0.03
(0.03 +0.005t for
0.06
for
0<t≤ 6
t> 6
(i)
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.
(ii) 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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