Sophia purchased a variable annuity contract with a purchase payment of $$100,000.$ Surrender charges begin with $7$ percent in the first year and decline by $1\mathrm{.}0$ percent each year. In addition, Sophia can withdraw $10$ percent of her contract value each year without paying surrender charges. In the first year, Sophia needed to withdraw $$16,500.$ Assume that the contract value had not increased or decreased because of investment performance. What was the surrender charge Sophia had to pay?