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

First, we need to determine the cost of buying and selling the securities over the three-month holding period. Since the transaction costs are given as $2,200, and the securities will be bought and sold once, we can assume that the total transaction costs for the investment are $2,200.

Next, we need to calculate the minimum annual yield required for the investment to make economic sense. We do this by comparing the transaction costs to the surplus funds.

The formula to calculate the required annual yield is as follows:
Required Annual Yield = (Transaction Costs / Surplus Funds) / (Holding Period / 12)

In this case, the transaction costs are $2,200, and the surplus funds are $200,000. The holding period is three months, which is equivalent to 3/12 = 0.25 years.

Plugging the values into the formula:
Required Annual Yield = ($2,200 / $200,000) / 0.25

Simplifying the expression:
Required Annual Yield = 0.011 / 0.25

Calculating the result:
Required Annual Yield ≈ 0.044 or 4.4%

Therefore, the required annual yield that must be earned before the investment makes economic sense is approximately 4.4%.