$$90,000$ reverse mortgage is for $10$ years at $8\%$ interest rate where payments are made annually at the end of each year. What portion of the loan balance at the end of year $10$ represents principal?

Between $50\%$ and $53\%$

Between $53\%$ and $56\%$

Between $56\%$ and $59\%$

Between $59\%$ and $62\%$

Between $62\%$ and $65\%$

Between $65\%$ and $68\%$

Between $68\%$ and $71\%$