Lilian opened a compound interest savings account when her daughter was born. She opened the account with an initial deposit of $$5,000,$ the account paid $4\mathrm{.}1\%$ annual interest and was compounded monthly. As one of her daughter's birthday presents Lilian closed the account and gave all the money from the account to her daughter. If Lilian gave her daughter $$17,070\mathrm{.}32261,$ how old was her daughter on that birthday?

Round your answer to the nearest whole year.

$32$ years old

$30$ years old

$35$ years old

$25$ years old