Sophia purchased a variable annuity contract with a purchase payment of $$105,000.$ Surrender charges begin with $6$ percent in the first year and decline by $2\mathrm{.}0$ percent each year. In addition, Sophia can withdraw $9$ percent of her contract value each year without paying surrender charges. In the first year, Sophia needed to withdraw $$16,150.$ Assume that the contract value had not increased or decreased because of investment performance. What was the surrender charge Sophia had to pay?

Surrender charge