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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