Question

The risk-free force of interest 𝛿(𝑡) at time 𝑡 is given by: 𝛿(𝑡)={ 0.03 𝑓𝑜𝑟 0<=𝑡<70.08 + 0.001𝑡 𝑓𝑜𝑟 7<=𝑡 (i) (a) Calculate the accumulation at time 9 of 𝐾1500 invested at time 𝑡=5. (b) Calculate the accumulation at time 6 of 𝐾4000 invested at time 𝑡=5. (c) Calculate the accumulation at time 15 of 𝐾1550 invested at time 𝑡=3. (d) Calculate the equivalent constant force of interest from time 𝑡=4 to time 𝑡=11. (ii) Calculate the present value at time 𝑡=0 of a continuous payment stream payable at a rate of 112𝑒0.005𝑡 from time 𝑡=0 to time 𝑡=5.

Name: the risk free force of interest t at time t is given by t 003 for 0t7008 0001t for 7t i a calculate the accumulation at time 9 of k1500 invested at time t5 b calculate the accumulation at ti 41997
Uploaded: 2022-05-14T05:27:13-08:00
Duration: 2 min 8 s
Channel: Minh Le
Description: the risk free force of interest t at time t is given by t 003 for 0t7008 0001t for 7t i a calculate the accumulation at time 9 of k1500 invested at time t5 b calculate the accumulation at ti 41997

          The risk-free force of interest 𝛿(𝑡) at time 𝑡 is given by:
𝛿(𝑡)={ 0.03 𝑓𝑜𝑟 0<=𝑡<70.08 + 0.001𝑡 𝑓𝑜𝑟 7<=𝑡
(i)
(a) Calculate the accumulation at time 9 of 𝐾1500 invested at time 𝑡=5.
(b) Calculate the accumulation at time 6 of 𝐾4000 invested at time 𝑡=5.
(c) Calculate the accumulation at time 15 of 𝐾1550 invested at time 𝑡=3.
(d) Calculate the equivalent constant force of interest from time 𝑡=4 to time 𝑡=11.
(ii) Calculate the present value at time 𝑡=0 of a continuous payment stream payable at a rate of 112𝑒0.005𝑡 from time 𝑡=0 to time 𝑡=5.

Added by Mireia W.

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