# Find The Formula For The Sum Of N Terms Calculator How Are You Doing With Your Retirement Liability?

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## How Are You Doing With Your Retirement Liability?

Pension managers and corporate treasurers use a funding strategy that matches the maturity of the asset with the maturity of the liability so they know they will have the cash they need to pay the debt when it comes due. If you think about this technique, you can use it to deal with your own pension or retirement obligations. Many of us no longer have a company-sponsored pension plan for our retirement. That responsibility has been transferred to us in one of the most serious transitions of corporate responsibility to employees. The alternative is now a self-funded 401k account.

You know what else happened with the return of corporate pensions? The sources that calculate the future value of the pension, the investment managers that look after the portfolio and the insurance company that manages the risk and the source of your pension payments through the annuity that the company buys for you. You have to do all this for yourself now. And getting good financial support is not easy.

So let me give you some help to get you started with computing your retirement liability. It is not complicated to do if you have a basic knowledge of time value of money concepts. I will do this in two steps: (1) explain how to calculate the liability and (2) calculate the funding gap to isolate any longevity risk.

Step 1: You must come up with an income in retirement that will sustain your standard of living.

Let’s use a current income of \$60,000 and your age is 40. Your goal is to retire at age 65. You want your money to last until the age of 100 – the ideal age for planning purposes so that you don’t take longevity risk. Longevity risk is the likelihood that you will outlive your retirement assets.

A \$60k income today won’t buy the same goods 25 years from now so we have to factor in inflation. Let’s say 3%. At age 65, the inflation-adjusted income is \$125,627. Calculated by standard future value calculations using a financial calculator where N (number of periods) is 25; I (interest rate) is 3% and PV (present value) is \$60,000. Solve for the FV (future value) and you get the result: \$125,627.

We’re not done yet. Next we calculate the pension liability. You need \$125,627 per year for the last 35 years; We still have to factor in inflation at 3%. Now the hard part. Expected rate of return on investment. You could write a whole book on how to figure it out. I’ll skip that and go to 7%, which I think is reasonable for long-term returns in our current market environment.

From these two numbers we calculate the inflation adjusted rate of return. It’s just a matter of dividing 1.07 by 1.03 and subtracting 1. In this case the factor is 3.883% – the rate that will tell you the value of the pension liability at age 65 adjusted for inflation. Enter N=35, I = 3.883%, Payment = \$125,627, FV =\$ 0 and solve for PV: \$2,474,997 (set the calculator at the beginning of the period to be more conservative).

To start retirement at age 65, maintain your current standard of living with an income of \$60k today adjusted for inflation over the past 35 years, accounting for inflation of 3% in retirement and earning an average return of 7% you need assets to mature. With a value of \$2,474,997 at age 65. This is your pension liability.

One final calculation. The amount we just calculated is what you’ll need 25 years from today – do you want to know what it’s worth today when you’re 40? The value \$456,017 is calculated as follows: FV (future value): \$2,474,997, N = 25, I = 7% Solving for PV = \$456,017. This is an amount that if deposited in a lump sum today would grow to \$465,017 at age 65 at 7%.

We have completed the first step. You now have an estimate of your pension liability 25 years into the future and its present day equivalent.

Step 2: Find out if you have a funding gap that exposes you to longevity risk after retirement.

A step of general arithmetic. Take the current account balance in any retirement account you have – 401k, SEP, SIMPLE, IRA, Roth IRA, money purchase, 403b, 457, profit sharing or any account you use to save money for retirement. Subtract this from today’s pension liability amount. If this is the case then this is your fund gap or surplus.

Let’s say it’s a gap. This is when financial planning begins.

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