Dave takes out a loan for $$5000$ to be repaid at the end of $9$ months. The simple interest rate on the loan is $r=9\%$ for the first two months, $r=12\%$ for

the next $6$ months, and $r=6\%$ thereafter. How much does Dave have to pay back at the end of $9$ months?

Multiple Choice

$$5337\mathrm{.}50$

$$5450\mathrm{.}00$

$$5225\mathrm{.}00$

$$5400\mathrm{.}00$