Susan wants to save money to buy a motorcycle. She invests in an ordinary annuity that earns $4.8\mathrm{\%}$ interest, compounded quarterly. Payments will be made at the end of each quarter.

How much money will she need to pay into the annuity each quarter for the annuity to have a total value of $\mathrm{\$}7000$ after 6 years?

Step 1 ：Susan wants to save money to buy a motorcycle. She invests in an ordinary annuity that earns 4.8% interest, compounded quarterly. Payments will be made at the end of each quarter. She wants the annuity to have a total value of $7000 after 6 years.

Step 2 ：We need to find out how much money she will need to pay into the annuity each quarter.

Step 3 ：We can use the formula for the future value of an ordinary annuity: $FV=P\times \frac{(1+r/n{)}^{n\times t}-1}{r/n}$, where $FV$ is the future value, $P$ is the payment made each period, $r$ is the annual interest rate, $n$ is the number of compounding periods per year, and $t$ is the number of years.

Step 4 ：We can rearrange this formula to solve for $P$: $P=FV\times \frac{r/n}{(1+r/n{)}^{n\times t}-1}$.

Step 5 ：Substituting the given values into the formula, we get: $P=7000\times \frac{0.048/4}{(1+0.048/4{)}^{4\times 6}-1}$.

Step 6 ：Solving this equation, we find that $P\approx 253.41$.

Step 7 ：Final Answer: Susan will need to pay approximately $253.41 into the annuity each quarter for the annuity to have a total value of $7000 after 6 years. So, the final answer is $\boxed{{\displaystyle 253.41}}$.