Nitai $($age $40)$ contributes $10$ percent of his $$80,000$ annual salary to a Roth $401($k$)$ account sponsored by his employer, AY Incorporated. AY Incorporated matches employee contributions dollar$-$for$-$dollar up to $10$ percent of the employee's salary. However, AY matches by contributing to the employee's traditional $401($k$)$ account because the employer contributions are not fully vested to the employee at the time of the contribution. Nitai expects to earn a $5$ percent before$-$tax rate of return.