JOHN has just celebrated his 24thbirthday. He has come to you for advice on investing for retirement. He has been offered several plans by different wealth advisors and he is confused. At the moment, he has just started his career and has started earning but between rent, eating out and paying for mobile phones it is a stretch. However, if he cuts non-essential expenses, he can save Rs. 20,000 per month.

Q1

PLAN A: This requires him to invest Rs. 20,000 per month in an equity fund every month for 10 years. The first investment will happen 1 month from now and the last investment will be on his 34thbirthday, making a total of 120 investments of Rs. 20,000 each. The expected return is an annual percentage rate of 15% with monthly compounding. After the 10thyear, there will be no more investments. The fund will payout the corpus on JOHN's 60thbirthday. (until then the sum of money accumulated in JOHN's account will continue to earn interest at the rate of 15% per annum with monthly compounding until the corpus is paid out.)

What is the expected value of the corpus, i.e. how much money can JOHN expect to withdraw on his 60thbirthday?

Q2

PLAN B: This plan does not require investments for 10 years. Starting from JOHN's 34thbirthday, he will start investing Rs. 20,000 in the equity fund. The last investment will be one month before his 60thbirthday. This will be a total of 312 investments of Rs. 20,000 each. The expected return is an annual percentage rate of 15% with monthly compounding. The fund will pay out the corpus on JOHN's 60thbirthday.

What is the expected value of corpus that JOHN will receive, i.e. how much money can JOHN expect to withdraw on his 60thbirthday?

Q.3

What explains the difference in the expected value of the corpus in PLAN A and PLAN B? What lessons can we infer about personal financial investments from these two plans?