In any given year, the rate of interest earned by an investor on her savings account...
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In any given year, the rate of interest earned by an investor on her savings account is independent rates in all previous years. Let i, denote the rate of interest earned in year t, and assume that (1+i) has a lognormal distribution with parameters, and of as follows: year, t 14 σ, 1 2 3 4 5 0.035 0.040 0.045 0.050 0.055 0.0005 0.0007 0.0009 0.0012 0.0016 (1) Suppose an investment of £250 is made at the beginning of the first year. Calculate the expected value and the standard deviation of the accumulated amount at the end of the first year. (1) (i) Define S, to be the accumulated amount at the end of year t for an initial investment of £1 made at the start of the first year. Find the distribution of In (S₂). Assuming that the investor has £1,000 to invest and requires a sum of £1,150 after five years, find the probability that she falls short of her target. In any given year, the rate of interest earned by an investor on her savings account is independent rates in all previous years. Let i, denote the rate of interest earned in year t, and assume that (1+i) has a lognormal distribution with parameters, and of as follows: year, t 14 σ, 1 2 3 4 5 0.035 0.040 0.045 0.050 0.055 0.0005 0.0007 0.0009 0.0012 0.0016 (1) Suppose an investment of £250 is made at the beginning of the first year. Calculate the expected value and the standard deviation of the accumulated amount at the end of the first year. (1) (i) Define S, to be the accumulated amount at the end of year t for an initial investment of £1 made at the start of the first year. Find the distribution of In (S₂). Assuming that the investor has £1,000 to invest and requires a sum of £1,150 after five years, find the probability that she falls short of her target.
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