St. Luke’s Convalescent Center has $200,000 in surplus funds that it wishes to invest in marketable securities. If transaction costs to buy and sell the securities are $2,200 and the securities will be held for three months, what required annual yield must be earned before the investment makes economic sense?

To determine the required annual yield, we need to consider the transaction costs and the holding period of the investment.

First, let's calculate the total transaction costs over the holding period. The transaction costs are given as $2,200. Since the securities will be held for three months, we need to convert the holding period to years. There are 12 months in a year, so three months is equivalent to 3/12 or 0.25 years.

Transaction costs over the holding period = Transaction costs * Holding period
Transaction costs over the holding period = $2,200 * 0.25
Transaction costs over the holding period = $550

Now, let's calculate the minimum investment yield required to cover the transaction costs. This yield should compensate for the transaction costs and provide a return on the investment.

Minimum required yield = Transaction costs over the holding period / Surplus funds
Minimum required yield = $550 / $200,000

To convert this to an annual yield, we multiply by 100 and divide by the holding period in years (0.25):

Minimum required annual yield = (Minimum required yield * 100) / Holding period in years
Minimum required annual yield = ($550 / $200,000) * 100 / 0.25

Now, let's compute the value:

Minimum required annual yield = 0.275% per year

Therefore, to make economic sense, the investment must earn a minimum annual yield of 0.275%.