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Probability
On your 40th birthday, you decide to start investing for retirement. On that date, you invest $1,000 in a stock index fund, and on each succeeding birthday through your 64th, you invest 10% more in the fund than you invested on your previous birthday. Assume that the return from the stock index fund in any given year is normally distributed with mean 4.5% and standard deviation 2.8%. For example, if the return in the first year is 2.7%, your $1,000 investment will grow to $1,027 by the end of the year. Assume the returns in different years are probabilistically independent. Assume that your goal is to have at least $150,000 in the fund by the time of your 65th birthday. After running a simulation with at least 5,000 replications, what is the most realistic conclusion about the probability that you will reach your goal? a. This probability is around 0.31. b. This probability is around 0.15. c. This probability is around 0.57. d. This probability is around 0.43.

On your 40th birthday, you decide to start investing for retirement. On that date, you invest $1,000 in a stock index fund, and on each succeeding birthday through your 64th, you invest 10% more in the fund than you invested on your previous birthday. Assume that the return from the stock index fund in any given year is normally distributed with mean 4.5% and standard deviation 2.8%. For example, if the return in the first year is 2.7%, your $1,000 investment will grow to $1,027 by the end of the year. Assume the returns in different years are probabilistically independent. Assume that your goal is to have at least $150,000 in the fund by the time of your 65th birthday. After running a simulation with at least 5,000 replications, what is the most realistic conclusion about the probability that you will reach your goal? a. This probability is around 0.31. b. This probability is around 0.15. c. This probability is around 0.57. d. This probability is around 0.43.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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On your 40th birthday, you decide to start investing for retirement. On that date, you invest $1,000 in a stock index fund, and on each succeeding birthday through your 64th, you invest 10% more in the fund than you invested on your previous birthday. Assume that the return from the stock index fund in any given year is normally distributed with mean 4.5% and standard deviation 2.8%. For example, if the return in the first year is 2.7%, your $1,000 investment will grow to $1,027 by the end of the year. Assume the returns in different years are probabilistically independent. Assume that your goal is to have at least $150,000 in the fund by the time of your 65th birthday. After running a simulation with at least 5,000 replications, what is the most realistic conclusion about the probability that you will reach your goal? a. This probability is around 0.31. b. This probability is around 0.15. c. This probability is around 0.57. d. This probability is around 0.43.
Transcribed Image Text:On your 40th birthday, you decide to start investing for retirement. On that date, you invest $1,000 in a stock index fund, and on each succeeding birthday through your 64th, you invest 10% more in the fund than you invested on your previous birthday. Assume that the return from the stock index fund in any given year is normally distributed with mean 4.5% and standard deviation 2.8%. For example, if the return in the first year is 2.7%, your $1,000 investment will grow to $1,027 by the end of the year. Assume the returns in different years are probabilistically independent. Assume that your goal is to have at least $150,000 in the fund by the time of your 65th birthday. After running a simulation with at least 5,000 replications, what is the most realistic conclusion about the probability that you will reach your goal? a. This probability is around 0.31. b. This probability is around 0.15. c. This probability is around 0.57. d. This probability is around 0.43.
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