\'Q3: Retirement Planning. A couple will retire in 50 years, which should last a

Question

'Q3: Retirement Planning. A couple will retire in 50 years, which should last about 25 years. They believe that they can earn 8% (nominal) interest on retirement savings but they realize that the annual inflation rate is 4%. The couple really wants to consume $30,000 a year in real dollars during retirement.

a)     What is the real amount of saving they need to accumulate by the time they retire?

b)    How much will they have to save each year for the next 50 years, in real dollars, to reach your retirement income goal? '

Please explain.

Explanation / Answer

a. The present value of the planned consumption stream as of the retirement date will be: $30,000 ? annuity factor(25, 8%) = $320,243.29
Therefore, they need to have accumulated this amount of savings by the time they retire. So, their savings plan must provide a future value of: $320,243.29
With 50 years to save at 8, the savings annuity must be: $558.14

Another way to think about this is to recognize that the present value of the savings stream must equal the present value of the consumption stream. The PV of consumption as of today is: $320,243.29/(1.08)50 = $6,827.98
Therefore, we set the present value of savings equal to this value, and solve for the required savings stream.
b. The couple needs to accumulate additional savings with a present value of:
$60,000/(1.08)20 = $12,872.89
The total PV of savings is now: $12,872.89 + $6,827.98 = $19,700.87
Now we solve for the required savings stream as follows:
Using a financial calculator, enter: n = 50; i = 8; PV = (-)19,700.87; FV = 0; and then compute PMT = $1,610.41

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