An investment fund is expected to grow over the next 10-year period at an annual interest rate that has the following probability distribution: i p.a. 2.5% 3.5% 5% 6% P (It = i) 0.2 0.3 0.4 0.1 Calculate the expected value and the standard deviation of the accumulated amount at the end of 10 years of a £200,000 investment held at time t = 0 under the following forecast scenarios: (i) It is assumed that the same annual interest rate applies to the fund over the entire term. (ii) It is assumed that in any year the rate of interest on the fund varies independently of the rates of interest in all previous years.
An investment fund is expected to grow over the next 10-year period at an annual interest rate that has the following probability distribution: i p.a. 2.5% 3.5% 5% 6% P (It = i) 0.2 0.3 0.4 0.1 Calculate the expected value and the standard deviation of the accumulated amount at the end of 10 years of a £200,000 investment held at time t = 0 under the following forecast scenarios: (i) It is assumed that the same annual interest rate applies to the fund over the entire term. (ii) It is assumed that in any year the rate of interest on the fund varies independently of the rates of interest in all previous years.
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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Question
Solve it using formulas, no tables
correct answers are;
i) E[ 200,000 x S(10) ] = 200,000 x 1.50984 = 301,967.8
SD[ 200,000 x S(10)] = 200,000 x 0.164555 = 32,910.97
ii) E[ 200,000 x S(10) ] = 200,000 x 1.501733 = 300,346.6
SD[ 200,000 x S(10) ] = 200,000 x 0.0520523 = 10,410.45
Transcribed Image Text:An investment fund is expected to grow over the next 10-year period at an annual interest
rate that has the following probability distribution:
i p.a.
2.5%
3.5%
5%
6%
P (It = i)
0.2
0.3
0.4
0.1
Calculate the expected value and the standard deviation of the accumulated amount at the
end of 10 years of a £200,000 investment held at time t = 0 under the following forecast
scenarios:
(i)
It is assumed that the same annual interest rate applies to the fund over the entire
term.
(ii)
It is assumed that in any year the rate of interest on the fund varies independently of
the rates of interest in all previous years.
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