You are 35 years old today and are considering your retirement needs. You expect to retire at age 65 (in 30 years) and you plan to live to 99. You want to buy a house costing 300,000 on your 65th birthday and your living expenses will be 30,000 a year after that (for 35 years), assume an annual interest rate of 8%, annual compounding:

How much will you need to have saved by your retirement date to be able to afford this?
Alternatively, suppose you already have 50,000 in savings today. If you can invest at 8% a year, how much would you need to save at the end of each year for the next 30 years to be able to afford this retirement plan?

Answer:

1)

We need to find the corpus at requirement which is required, to be able to buy a house worth 300,000 and sustain a living for which I need 30,000 per year for the next 35 years. Lets calculate how much corpus we need to sustain a living.

Per Year payment required is $30,000

Time is 35 years

With a simple formulae in excel of PV(8%,35,30000) we get the present value of these cash flows as $349,637 which we require so that we get $30,000 payment per year for the next 35 years. Now we also need to purchase a house worth $300,000 on retirement. We simply add both amounts and total amount which we require at retirement is $649,637 so that my both the goals are acomplished.

2)

So now we already have 50,000 in savings account. Let X be the amount of saving for the next 30 years which I need to do. with Interest rate 8% and FV of $649,637.

Here we apply the PMT formulae in excel to calculate the per year amount which we need to save to reach our goal.

PMT (8%,30,50000,-649637) = $1293.26 which means that we need to save $1293.26 every year so that our corpus at the time of retirement (in 30 years) is $649,637

In PMT formule we need to pay special attention to the sign of the numbers. Present value of 50,000 will be positive as we are giving away this money today, Future value of $649,637 needs to be (-) as will be receiving that money after 30 years and we will see that when we punch these numbers in excel, 1,293 will be positive which indicates that we will invest this amount per year.