A trust fund for a $8-$year$-$old grandchild is being set up by her grandfather. The objective of the grandfather is to have $$120,000$ when she is $18,$ that is after $10$ years.

The grandfather is investing a fixed amount at the end of each quarter. If the fund earns APR of $7\mathrm{.}25\%,$ how much money should be invested into the fund at every quarter end?

$$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($calculate to cents$)$