Question

Each student should answer question 1 A and 1 B. Answer to the question 1 is related to your actual age. Simplify your age to the month, if for example your age is 20 years 1 month and 19 days, use 20 years and 2 months. If your age is 34 years and one month and 3 days, use 34 years and one month, in other words, bring your age to closest month.

(Age is 28 years and 6 months) Assume you drink one coffee per day, 5 days a week. Assume coffee price is $4.00. That makes it $20 per week and $80 per month. Assume you can invest $80 per month in the stock market and assume you can earn 1 % per month on your stock investment or 12 % per year.

A:  At your retirement, when you are 65 years old, how much you will have in your retirement account if you switch from coffee drinking to investing in the stock market?

B. Assume that when you get to 65 (retirement age) you switch your funds from stock market investment to bond market investment.Assume you can earn 7% on your bond investment. You decide to withdraw a constant amount each year for the next 20 years when you get to retirement age of 65. How much will be your annual withdrawal from age 66 to 85 (Nothing left at 85) if you switch your coffee drinking to stock and bond investments.

Answer 1

(a) Current Age is assumed to be 28 years 6 months (as mentioned in the question).

Retirement age is assumed to be 65 years.

Total Time Period of Stock Investment = 65 - 28.5 = 36.5 years or 438 months

Stock Returns =1% per months or 12% per year.

NOTE: The stock investment amount is assumed to be compounded every months therefore giving an annual percentage yield (APY) of (1.01)^(12) = 12.68% instead of the stated 12%. This essentially means that 12% is the APR(Annual Percentage Return) or nominal rate of return. Actual returns is higher at 12.68%.

Investment amount for a month = Cost of Coffee Consumed in a month = $ 80 (as calculated)

Now the first month's investment comes in at the end of 28 years and 7 months ( and not 28 years and 6 months as I save for the 7th month of the 28th year of my life and at the end of that month make my first stock investment of $80). This investment will be compounded for a period of 437 months. The next one will be compounded for 436 months and so on.

Therefore, value of stock investments at retirement = FV(65) = 80 x (1.01)^(437) + 80 x (1.01)^(436) + 80 x (1.01)^(435) + ......+ 80

= [({(1.01)^(438)} - 1) / (1.01 - 1)] x 80

= $ 616959.2548

(b) The switch from stock to bond investment entails that I receive a fix amount say $ K per annum and this new investment earns an annual return of 7%. This implies that after retirement I receive equal annual cash flows starting at age 66 and ending at age 85 thereby forming a 20 year annuity cash flow. These cash flows when discounted at the annual return rate of 7% should be equal to the saved amount of FV(65) (calculated in part(b)).

FV(65) = K x (1/0.07) x [1 - {1/(1.07)^(20)}]

616959.2548 = K x (1 / 0.07) x [1 - {1/(1.07)^(20)}]

K = $ 58236.5891