The force of interest 8(t) at any time t, measured in years, is given by: (0.02 +0.003t² for 0 6 8(t) = 0.4-0.02t (i) Derive, and simplify as far as possible, expressions in terms of t for the present value of a unit investment made at time t. You should derive separate expressions for sub- intervals 0 < t ≤6 and t> 6. (ii) Hence, calculate the accumulated value at time t = 12 of £500 due for payment at time t = 4. (iii) Calculate the constant annual nominal rate of interest convertible quarterly implied by the transaction in part (ii).
The force of interest 8(t) at any time t, measured in years, is given by: (0.02 +0.003t² for 0 6 8(t) = 0.4-0.02t (i) Derive, and simplify as far as possible, expressions in terms of t for the present value of a unit investment made at time t. You should derive separate expressions for sub- intervals 0 < t ≤6 and t> 6. (ii) Hence, calculate the accumulated value at time t = 12 of £500 due for payment at time t = 4. (iii) Calculate the constant annual nominal rate of interest convertible quarterly 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:
(0.02 +0.003t2²
(0.4 -0.02t
for 0<t≤6
for t> 6
8(t)
= {0.02
(i) Derive, and simplify as far as possible, expressions in terms of t for the present value
of a unit investment made at time t. You should derive separate expressions for sub-
intervals 0 < t ≤6 and t> 6.
(ii) Hence, calculate the accumulated value at time t = 12 of £500 due for payment at
time t = 4.
(iii) Calculate the constant annual nominal rate of interest convertible quarterly implied by
the transaction in part (ii).
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