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 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) (iv) Calculate, to the nearest 0.1%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii). 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
Question

PLEASE, WRITE THE SOLUTIONS ON PAPER, EXPLAINING THE ENTIRE PROCESS, THE ONLY POSSIBLE SOLUTIONS ARE THE STIPULATED ONES

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
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
(0.03 +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)
(iv)
Calculate, to the nearest 0.1%, the constant nominal annual rate of interest
convertible half-yearly implied by the transaction in part (ii).
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.
Transcribed Image Text: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 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 (0.03 +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) (iv) Calculate, to the nearest 0.1%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii). 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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