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How much can Mr. Road spend each year? First let’s see what happens if we ignore inflation.
1. Account for Social Security income of $750 per month, or $9,000 annually.
2. Account for the income from the savings account. Because Mr. Road does not want to run down the balance of this account, he can spend only the interest income:
0.05 ? $12,000 = $600 annually
3. Compute the annual consumption available from his investment account. We find the 20-year annuity with present value equal to the value in the account:
Present Value = annual payment ? 20-year annuity factor at 9% interest rate:
PV = annual payment
$180,000 = annual payment ? 9.129 ? Annual payment = $180,000/9.129 = $19,717
Notice that the investment account provides annual income of $19,717, which is more than the annual interest from the account. This is because Mr. Road plans to run the account down to zero by the end of his life.
So Mr. Road can spend: $19,717 + $600 + $9,000 = $29,317 per year
This is comfortably above his current living expenses, which are $2,000 per month or $24,000 annually.
The problem of course is inflation. We have mixed up real and nominal flows. The Social Security payments are tied to the consumer price index and therefore are level in real terms. But the annuity of $19,717 per year from the investment account and the $600 interest from the savings account are fixed in nominal terms, and therefore the purchasing power of these flows will steadily decline.
For example, let’s look out 15 years. At ...