$(,2\mathrm{.}1)$

A company needs $$150,000$ each year for regular payments. Converting the company's short$-$term investments into cash to meet these regular payments incurs a fixed cost of $$400$ per transaction. These short$-$term investments pay interest of $5\%$ per year, while the company earns interest of only $1\%$ per year on cash deposits.

According to the Baumol Model, what is the optimum amount of short$-$ term investments to convert into cash in each transaction?

$$38,730$

$$48,990$

$$54,772$

$$63,246$