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Lifetime Benefits and Taxes in Social Security: The Effect of Different Discount Rates on Present Value Calculations

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Document date: February 18, 2011
Released online: February 22, 2011

Abstract

It is often useful to compute contributions and benefits over a lifetime when studying policies for retirement and Social Security. However, these calculations are complicated by factors like economic growth and inflation, which change the relative value of investments over time. The fact that $1 in the bank today might accrue enough interest to be worth $1.03 next year leads economists, accountants, and actuaries to find ways to equate the two amounts at a point in time. This fact sheet explains how the discount rate affects present value calculations.

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Introduction

It is often useful to compute contributions and benefits over a lifetime when studying policies for retirement and Social Security. However, these calculations are complicated by factors like economic growth and inflation, which change the relative value of investments over time. The fact that $1 in the bank today might accrue enough interest to be worth $1.03 next year leads economists, accountants, and actuaries to find ways to equate the two amounts at a point in time. That is, they try to find the value of an account today that might provide the stream of benefits to be paid out tomorrow, assuming some interest would be paid on the account. A similar calculation can be made on how much a worker paid in taxes or contributions over a lifetime, depending upon the interest earned on those contributions.

Consider first a situation where there is 0 percent real interest or one simply wants to know the real value of all future benefits without treating $1 tomorrow as worth less today. In Social Security, the real value of benefits is held constant each year after retirement through a cost-of-living adjustment. Take a male worker who has earned the average wage over his entire lifetime, who turns 65 in 2010, and who remains in retirement for an average remaining lifespan of approximately 18 years. His annual Social Security benefits would be approximately $17,400 in real (inflation-adjusted) terms. The worker's benefits are paid as an annuity over his remaining lifetime, however long it turns out to be: one worker might live 14 years and another 22 years, but together they will average 18 years of payment. Because here we assume a real interest rate of zero, the real value of benefits and the present value of the Social Security benefits the typical worker would expect to receive over his lifetime would be approximately $314,000 (or, roughly, 18 times $17,400; figure 1). Said differently, if this worker in 2010 were going to purchase an annuity from which he expects to receive $17,400 annually, but received no interest on his account, it would cost $314,000. However, if the money were sitting in a bank account or an account with an insurance company, it likely would earn interest until it was withdrawn. In this situation, the present value calculation must adjust for some real rate of return. If that rate were 2 percent, then the male worker who receives $17,400 in annual Social Security benefits could buy his total Social Security "annuity" for about $256,000 in 2010 on this discounted basis. If instead the real rate of return were 3 percent, the present value of the lifetime benefits would be approximately $234,000. The higher the real rate of return, the lower the "price" of the total annuity in present value terms.

We can do the same for taxes. If one adds up the taxes the worker pays, excluding any interest that might have been earned on those contributions, the total tax burden adds up to almost $192,000. At a 2 percent or 3 percent real return, those contributions would have grown to approximately $291,000 and $364,000, respectively, by 2010.

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Topics/Tags: | Employment | Retirement and Older Americans


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