# Retirement Funding – An Example

Retirement Funding – An Example

Introduction

This example examines funding retirement through appropriate levels of savings made during the active earning (pre-retirement) period of an individual’s life. In order to clarify the example, this section provides a brief overview of the relevant theory.

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The primary concepts involved are those of present value and future value. A dollar that is invested today (that is, a present value of $1) will earn interest, and therefore in the future, will be worth more than one dollar (future value). The difference in values is dependent on the interest rate, i. Thus, the future value (FV1) at the end of one year equals the present value (PV) multiplied by 1 plus the interest rate, i.e.

FV1 = PV (1 + i)

At the end of n years, the future value (FVn) is given by the formula (Brigham, Gapenski, and Erhardt, 1999; pg 247):

FVn = PV (1 + i)n

Thus, by investing a suitable amount of money (PV) and leaving it to earn interest for n years, a lump sum FVn will be available for retirement at the end of the n-year period.

For most people, however, such a method of funding retirement will not be practical, as they are unlikely to have a suitably large amount to invest at a single time. A more practical approach thus involves many periodic investments spread out over the n-year period. For instance, a specific amount that is invested each month, as is considered in the example below. The following assumptions are made in the example:

The individual’s current income is assumed to be $10,000 per month.

It is assumed that the individual will require 75% of his current monthly income during retirement, i.e. $7,500 per month.

The individual is currently 30 years old, thus has 35 years till retirement at the age of 65.

An average annual interest rate of 7.5% is assumed for the investment.

Finally, it is assumed that the individual will have 20 years of retired life.

To simplify the example, it is also assumed that the investment plan proposed is the individual’s only source of retirement income and that all the money must be available at the time he reaches retirement age. Further, all monthly payments are made at the end of the month.

Future Value of Investment

The future value (FV420) of the investment is the amount of money required during the retirement period. From the assumptions above, the individual will require $7,500 per month for 20 years (240 months), thus giving a total requirement of 240 x $7500 = $1,800,000.

That is, the individual requires $1,800,000 to fund his retirement, under the assumptions given above.

Required Monthly Payments

To achieve this above retirement fund of $1,800,000, the individual has 35 years (i.e. 420 months) of monthly payments, PMT. This section will calculate the appropriate level of monthly investment required, by determining the value of PMT.

The future value of the monthly investments is given by the formula (Brigham, Gapenski, and Erhardt, 1999; pg 251):

FV420 = PMT(1+i)419 + PMT(1+i)418 + PMT(1+i)417 + … + PMT(i+i)

= PMT ( (1+i)420 – 1) / i

Here, I = 7.5% (p.a. = .075/12 p.m. = 0.00625 p.m.). Thus, the equation becomes:

1,800,000 = PMT ( (1+0.00625)420 – 1) / (0.00625)

= PMT ( 1.00625420 – 1 ) / (0.00625)

= PMT ( 13.6922 – 1 ) / (0.00625) = PMT (2030.7620)

Thus:

PMT = 1800000 / 2030.7620

= 886.37

That is, the individual must make payments of $886.37 per month for the period of 420 months remaining before retirement, in order to fund the total required retirement fund of $1,800,000.

Present Value of Retirement Funds

The present value (PV) of the $1,800,000 required at retirement is given by the following formula (using the manual discounting method; Brigham, Gapenski, and Erhardt, 1999; pg 254):

PV = FV / (1 + i)420

= (1800000) / ( 1 + 0.00625)420

= 131461.11

Thus, if the individual were to try and fund his retirement requirement of $1,800,000 with a single payment made now, he would need to invest the sum of $131,461.77.

References

· Brigham, E.F., Gapenski, I.L., and M.C. Erhardt. 1999. Financial Management: Theory and Practice. Dryden Press. Fort Worth. Texas.