The force of interest 8(t) at any time t, measured in years, is given by: for for for (i) (ii) 8(t) = 0.04e0.02t 0.03 +0.001t 0.045 0 < t ≤ 10 15 10 < t ≤ t> 15 Derive, and simplify as far as possible, expressions in terms of t for V (t), where V (t) is the present value of a unit sum of cash flow made at time t. You should derive separate expressions for the three sub-intervals. Hence, making use of the result in part (i), calculate the value at time t = 3 of a payment of £2,500 made at time t = 15. (iii) Calculate, to the nearest 0.01%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii).
The force of interest 8(t) at any time t, measured in years, is given by: for for for (i) (ii) 8(t) = 0.04e0.02t 0.03 +0.001t 0.045 0 < t ≤ 10 15 10 < t ≤ t> 15 Derive, and simplify as far as possible, expressions in terms of t for V (t), where V (t) is the present value of a unit sum of cash flow made at time t. You should derive separate expressions for the three sub-intervals. Hence, making use of the result in part (i), calculate the value at time t = 3 of a payment of £2,500 made at time t = 15. (iii) Calculate, to the nearest 0.01%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The force of interest 8(t) at any time t, measured in years, is given by:
for
for
for
(i)
(ii)
8(t)
0.04e0.02t
0.03 +0.001t
0.045
0 < t ≤ 10
15
10 < t ≤
t > 15
Derive, and simplify as far as possible, expressions in terms of t for V (t), where V (t) is
the present value of a unit sum of cash flow made at time t. You should derive separate
expressions for the three sub-intervals.
Hence, making use of the result in part (i), calculate the value at time t = 3 of a payment of
£2,500 made at time t = 15.
(iii) Calculate, to the nearest 0.01%, the constant nominal annual rate of interest convertible
half-yearly implied by the transaction in part (ii).
(iv) Making use of the result in part (i), calculate the present value of a payment stream p(t)
paid continuously from time t = 15 to t = 20 at a rate of payment at time t given by:
p(t) = 300e0.02t
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