Retirees generally tend to migrate to 'lower risk' investment options e.g. bonds, certified deposit- and/or 'high-yield' savings accounts.
Money in the bank is probably the worst investment choice, even worse than the much higher risk of e.g. investing in that same bank's stock. Instead of putting your money into the bank's savings account… you should rather consider buying the bank's stock!
By way of an example, the Bank of America ($BAC) Platinum Money Market Savings Account offers an annual percentage yield (interest rate earned) of 0.12% on balances of between $20,000-30,000. It would be unfair for me to simply state that $30,000 invested in $BAC stock for one year (2012), would have been worth $60,000 today… 2012 was an extraordinary year, delivering 100% returns for $BAC shareholders.
Also unfair would be for me to offset gains in $BAC above, with losses suffered in 2008/9 - the stock had lost ~90% of its value during that period, from $30 down to $3 (not nice, especially for a retiree!).
But $BAC was an outlier, so I'll pick another bank… a 'more stable one', J.P. Morgan Chase ($JPM), America's largest bank:
Currently, Chase Plus Savings offers a 0.20% on balances between $25,000 and $50,000. However in the early 2000's the savings account rates were higher, so - for the sake of this example - I will average the savings account interest rate at 1%.
$30,000 invested at 1% over 10 years compounded (meaning you earn interest also on your interest, every year), would be worth $33,138, for a gain (return on investment) of $3,138.
According to YCharts, 10 years ago (March 21 2003), JP Morgan stock was valued at $18.56/share. $30,000 would have allowed you to snag about 1,616 shares (+ approximately $10 for brokerage commission).
Today (March 22 2013) JP Morgan stock closed at $48.78, meaning that 1,616 shares would be worth $78,000 (with reinvested dividends) - i.e. more than double the original investment.
But you may ask "What if I had picked $BAC instead of $JPM? I may have lost money". Yes, that would be possible… and yes, you could pick 'the wrong' stock, much like you could pick the wrong mutual fund, bond, or leave your money in a savings account!
A better solution would have been to diversify and pick e.g. 3 banks, like 'uber conservative' Wells Fargo, 'middle of the conservative range' J.P. Morgan, and 'flying too close to sun' Bank of America.
Even better may have been to diversify even further and select a couple of blue-chip heavyweights (see part 2) that have traditionally delivered a good return. That way one could complement the bank stocks above with e.g. General Electric, Pfizer and Chevron.
Still nervous? Add three more, across different industries once more, like Caterpillar, Home Depot and Wal-Mart. For good measure (and further risk mitigation), add a tenth one, e.g. 3M Co., and you would have successfully built your own 'bulletproof' index of 10 Dow Jones Industrial Index ("Dow") stocks.
Together, these should provide enough risk mitigation, and reasonable returns, allowing you to top the rate on a savings account by >5% annually, without burdening yourself with too much stress. Just don't panic and start selling your stocks when they go down a little!
Also read "Should Retirees Buy Stocks (part 2)?" for a short analysis and an example that may help retirees select a Dow stock for investment. When you read the information provided, do not fret too much if I have used financial terms that you don't understand - the Dow only includes 30 stocks, so selecting 10 for your own portfolio wouldn't be too much of a challenge.
Note that all the companies mentioned in this post are Dow stocks. This index of 30 stocks is regarded as a leading market indicator, referred to on a daily basis as 'the market' ("the market was up/down 20 points today" actually means the Dow was up/down 20 points). Multi-billion dollar, American blue-chip companies that have stood the test of time… quite often, much better so than your local bank, that may not even still be in existence today.
The Dow index has historically returned, on average, about 6.8% annually for over 100 years. There will always be outliers (like Bank of America and H.P.)* included in any index, but as long as you pick e.g. 8 others, you should always be able to easily outperform any savings account offer from your local bank - where do you think the bank invests your money, in order to pay you 1% interest on your savings deposits?
* Last year's Dow loser was H.P., but this company happens to be this year's Dow leader in terms of return on investment. Conversely, Bank of America was last year's leader, although it's performance is looking decidedly more ordinary this year.