To model the future performance of an investment fund in the next 10 years, you assume...

 

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To model the future performance of an investment fund in the next 10 years, you assume that in each of the first 5 years, the effective rate of interest will be 4% or 8% per annum, with respective probabilities 0.25 and 0.75. From the 6th year, the annual effective rate of interest is distributed with probability density f) = 12.5 (50x1) for 0.02 ≤ x ≤0.06 62.5 (110x) for 0.06 ≤ x ≤ 0.1 Effective interest rates will be independent of that in any other such one-year period. (1) Find the mean value and standard deviation of the accumulation of a single pre- mium of £1,000 made at the start of the first year, at the end of the 5th year and at the end of 10th years. [8 pts] (2) Let X be the accumulated amount at the end of 10 years of a single investment of £1,000 made at the start of the first year. Use 2,000 simulations of X for each period to estimate the probability that X is less than £2,000, and give 95% confidence limits for this probability. [10 pts] (3) Find the mean and standard deviation of the accumulated amount at the end of 5th and 10th year of an annual investment of £1,000 made at the start of each year. [8 pts] (4) Let Y be the accumulated amount at the end of 10 years of an annual investment of £1,000 made at the start of each year. Use 2, 000 simulations of Y for each period to estimate the probability that Y is greater than 13, 500 and give 95% confidence limits for this probability. [10 pts] (5) Suppose that in each year of the first 5 years, the effective interest rate is 0.06. Without using simulation, calculate the probability that the accumulated amount at the end of 6th year of a single investment of £1,000 made at the start of the first year is less than 1400. [4 pts] To model the future performance of an investment fund in the next 10 years, you assume that in each of the first 5 years, the effective rate of interest will be 4% or 8% per annum, with respective probabilities 0.25 and 0.75. From the 6th year, the annual effective rate of interest is distributed with probability density f) = 12.5 (50x1) for 0.02 ≤ x ≤0.06 62.5 (110x) for 0.06 ≤ x ≤ 0.1 Effective interest rates will be independent of that in any other such one-year period. (1) Find the mean value and standard deviation of the accumulation of a single pre- mium of £1,000 made at the start of the first year, at the end of the 5th year and at the end of 10th years. [8 pts] (2) Let X be the accumulated amount at the end of 10 years of a single investment of £1,000 made at the start of the first year. Use 2,000 simulations of X for each period to estimate the probability that X is less than £2,000, and give 95% confidence limits for this probability. [10 pts] (3) Find the mean and standard deviation of the accumulated amount at the end of 5th and 10th year of an annual investment of £1,000 made at the start of each year. [8 pts] (4) Let Y be the accumulated amount at the end of 10 years of an annual investment of £1,000 made at the start of each year. Use 2, 000 simulations of Y for each period to estimate the probability that Y is greater than 13, 500 and give 95% confidence limits for this probability. [10 pts] (5) Suppose that in each year of the first 5 years, the effective interest rate is 0.06. Without using simulation, calculate the probability that the accumulated amount at the end of 6th year of a single investment of £1,000 made at the start of the first year is less than 1400. [4 pts] To model the future performance of an investment fund in the next 10 years, you assume that in each of the first 5 years, the effective rate of interest will be 4% or 8% per annum, with respective probabilities 0.25 and 0.75. From the 6th year, the annual effective rate of interest is distributed with probability density f) = 12.5 (50x1) for 0.02 ≤ x ≤0.06 62.5 (110x) for 0.06 ≤ x ≤ 0.1 Effective interest rates will be independent of that in any other such one-year period. (1) Find the mean value and standard deviation of the accumulation of a single pre- mium of £1,000 made at the start of the first year, at the end of the 5th year and at the end of 10th years. [8 pts] (2) Let X be the accumulated amount at the end of 10 years of a single investment of £1,000 made at the start of the first year. Use 2,000 simulations of X for each period to estimate the probability that X is less than £2,000, and give 95% confidence limits for this probability. [10 pts] (3) Find the mean and standard deviation of the accumulated amount at the end of 5th and 10th year of an annual investment of £1,000 made at the start of each year. [8 pts] (4) Let Y be the accumulated amount at the end of 10 years of an annual investment of £1,000 made at the start of each year. Use 2, 000 simulations of Y for each period to estimate the probability that Y is greater than 13, 500 and give 95% confidence limits for this probability. [10 pts] (5) Suppose that in each year of the first 5 years, the effective interest rate is 0.06. Without using simulation, calculate the probability that the accumulated amount at the end of 6th year of a single investment of £1,000 made at the start of the first year is less than 1400. [4 pts] To model the future performance of an investment fund in the next 10 years, you assume that in each of the first 5 years, the effective rate of interest will be 4% or 8% per annum, with respective probabilities 0.25 and 0.75. From the 6th year, the annual effective rate of interest is distributed with probability density f) = 12.5 (50x1) for 0.02 ≤ x ≤0.06 62.5 (110x) for 0.06 ≤ x ≤ 0.1 Effective interest rates will be independent of that in any other such one-year period. (1) Find the mean value and standard deviation of the accumulation of a single pre- mium of £1,000 made at the start of the first year, at the end of the 5th year and at the end of 10th years. [8 pts] (2) Let X be the accumulated amount at the end of 10 years of a single investment of £1,000 made at the start of the first year. Use 2,000 simulations of X for each period to estimate the probability that X is less than £2,000, and give 95% confidence limits for this probability. [10 pts] (3) Find the mean and standard deviation of the accumulated amount at the end of 5th and 10th year of an annual investment of £1,000 made at the start of each year. [8 pts] (4) Let Y be the accumulated amount at the end of 10 years of an annual investment of £1,000 made at the start of each year. Use 2, 000 simulations of Y for each period to estimate the probability that Y is greater than 13, 500 and give 95% confidence limits for this probability. [10 pts] (5) Suppose that in each year of the first 5 years, the effective interest rate is 0.06. Without using simulation, calculate the probability that the accumulated amount at the end of 6th year of a single investment of £1,000 made at the start of the first year is less than 1400. [4 pts] To model the future performance of an investment fund in the next 10 years, you assume that in each of the first 5 years, the effective rate of interest will be 4% or 8% per annum, with respective probabilities 0.25 and 0.75. From the 6th year, the annual effective rate of interest is distributed with probability density f) = 12.5 (50x1) for 0.02 ≤ x ≤0.06 62.5 (110x) for 0.06 ≤ x ≤ 0.1 Effective interest rates will be independent of that in any other such one-year period. (1) Find the mean value and standard deviation of the accumulation of a single pre- mium of £1,000 made at the start of the first year, at the end of the 5th year and at the end of 10th years. [8 pts] (2) Let X be the accumulated amount at the end of 10 years of a single investment of £1,000 made at the start of the first year. Use 2,000 simulations of X for each period to estimate the probability that X is less than £2,000, and give 95% confidence limits for this probability. [10 pts] (3) Find the mean and standard deviation of the accumulated amount at the end of 5th and 10th year of an annual investment of £1,000 made at the start of each year. [8 pts] (4) Let Y be the accumulated amount at the end of 10 years of an annual investment of £1,000 made at the start of each year. Use 2, 000 simulations of Y for each period to estimate the probability that Y is greater than 13, 500 and give 95% confidence limits for this probability. [10 pts] (5) Suppose that in each year of the first 5 years, the effective interest rate is 0.06. Without using simulation, calculate the probability that the accumulated amount at the end of 6th year of a single investment of £1,000 made at the start of the first year is less than 1400. [4 pts] To model the future performance of an investment fund in the next 10 years, you assume that in each of the first 5 years, the effective rate of interest will be 4% or 8% per annum, with respective probabilities 0.25 and 0.75. From the 6th year, the annual effective rate of interest is distributed with probability density f) = 12.5 (50x1) for 0.02 ≤ x ≤0.06 62.5 (110x) for 0.06 ≤ x ≤ 0.1 Effective interest rates will be independent of that in any other such one-year period. (1) Find the mean value and standard deviation of the accumulation of a single pre- mium of £1,000 made at the start of the first year, at the end of the 5th year and at the end of 10th years. [8 pts] (2) Let X be the accumulated amount at the end of 10 years of a single investment of £1,000 made at the start of the first year. Use 2,000 simulations of X for each period to estimate the probability that X is less than £2,000, and give 95% confidence limits for this probability. [10 pts] (3) Find the mean and standard deviation of the accumulated amount at the end of 5th and 10th year of an annual investment of £1,000 made at the start of each year. [8 pts] (4) Let Y be the accumulated amount at the end of 10 years of an annual investment of £1,000 made at the start of each year. Use 2, 000 simulations of Y for each period to estimate the probability that Y is greater than 13, 500 and give 95% confidence limits for this probability. [10 pts] (5) Suppose that in each year of the first 5 years, the effective interest rate is 0.06. Without using simulation, calculate the probability that the accumulated amount at the end of 6th year of a single investment of £1,000 made at the start of the first year is less than 1400. [4 pts]

Answer rating: 100% (QA)

1The mean value is 10001045108511251165125512768 The standard deviation is 10001045112521085112521125112521165112521251125255024 2 The answer is There ... View the full answer