Question

You have to set up your own retirement fund and aim to invest in a diversified portfolio of stocks of your choosing. In order to reduce the transaction costs of your investing you have estimated that you need to have a minimum of $100,000 to invest into your portfolio in 5 years. To achieve this target you aim to save the money from your pay, which you will deposit, in equal monthly instalments, in a medium-term cash account offering a nominal rate of 3% per annum compounded monthly.

a) Calculate how much you need to invest on a monthly basis in order to have the $100,000 available to invest in five (5) years.

Accruing this amount of money is the 1st step in your plans for retirement, however, this amount is only a stepping stone as you realise that this will be insufficient for your retirement in 35 years. Given that you are aiming to invest in a diversified manner, you expect that you will achieve a rate of return similar to the market portfolio. You estimate that you can achieve a rate of return on your portfolio of 7% per annum, compounded monthly.

Note: You will not be investing more money, from your wages, into your portfolio as you are confident of your ability to generate returns and you wish to invest the money into other assets.

As indicated, you expect that you will have a working life of 35 years from today, after which you expect you will need a need a minimum of $6,000 per month to live comfortably, in retirement, for a following 25 years. For simplicity, assume that the $6,000 per month payment will be made at the end of the month. Hint: Use a basic timeline to detail the cash flows.

b) Identify, using applicable calculations, whether you will have enough money (in the form of your portfolio investment) to support your $6,000 per month retirement allowance

Answer 1

The discounting factor is 3% per annum, which makes it 0.25% per month. So here consider the future value for the investment after 5 years is $100,000 (which is the amount that is required at the end of year 5). The question requires that interest is compounded monthly, so we shall take interest as 0.25% for 60 monthly periods.

The present value annuity factor for 60 periods at 0.25% is 55.6521. This is the sum of the monthly discounting factors at 0.25% for each period.

e.g. 1/(1.025)¹+1/(1.025)²+1/(1.025)³+1/(1.025)⁴+............ so on and so forth. This should go on till the power is 60.

So coming to our main question, if we want to calculate amount to be saved monthly to receive $100,000 at the end of year 5 - [100,000/55.6521]=$1,797 (this will be an approximate answer as there is a lot of approximation involved here.

Consider the below timeline for the sequence of events

If $1,797 is saved each month from now upto 35 years from now, and the return generated on these savings is 7% per annum (i.e. 0.583% per month), the amount that will be available at the end of the year will be $3,255,375.

The first $1,797 saved at the end of the first month will generate 0.0583% each month for 420 months (35yrs*12).

The second $1,797 saved at the end of the first month will generate 0.0583% each month for 419 months. and so on and so forth.

So,if $3,225,375 is available at the end of 35 years the return generated on the same per month at 7% per annum (0.583% per month) will be $18,990, which is more than the desired $6,000 per month.