Question

TO UNDERSTAND HOW IMPORTANT IS TO START AND SAVE EARLY CONSIDER ALSO THE FOLLOWING:

Find the accumulated value at 56 under the following to scenarios.

Scenario 1

You enter the plan at 40 and you participate for 10 years 2000 TL per year. Then you leave the accumulated funds to grow with interest until you are eligible for retirement.

Scenario 2

You enter the plan at 30 and you participate for 10 years 2000 TL per year. Then you leave the accumulated funds to grow with interest until you are eligible for retirement.

Note that in both cases you have participate ONLY for 10 years.

Answer 1

Scenario 1

Since the interest rate is not given, let us assume it as 12%

The formula for calculating the accumulated fund is for the periodic payments:

P = PMT [((1 + r)n - 1) / r]

Where:

P = Accumulated Fund
PMT = The amount of each annual payment = 2000
r = The interest rate = 12%
n = The number of periods over which payments are made = 10

P = 2,000 [((1 + 0.12)10 - 1) / 0.12] = 170,000

At the age of 49, the accumulated fund is 170,000

Time left for retirement 56-49 = 7 years

The amount accumulated at the retirement age =

where 'r' is the interest rate and 'n' is the number of years.

= 375,815.84

Scenario 2

We shall assume the investment parameters the same as the previous case.

P = PMT [((1 + r)n - 1) / r]

P = 2,000 [((1 + 0.12)10 - 1) / 0.12] = 170,000

At the age of 39, the accumulated fund is 170,000

Time left for retirement 56-39 = 17 years

The amount accumulated at the retirement age =

where 'r' is the interest rate and 'n' is the number of years.

= 1,167,226.95

There is a wide difference in the amount accumulated at the retirement age. Starting the investment 10 years early (keeping the investment parameters same) can make a huge difference. In this case, the amount accumulated in the second scenario was more than three times the first one.