Matthew $(48$ at year$-$end$)$ develops cutting$-$edge technology for SV Incorporated, located in Silicon Valley. In $2023,$ Matthew participates in SV$\text{'}$s money purchase pension plan $($a defined contribution plan$)$ and in his company's $401($k$)$ plan. Under the money purchase pension plan, SV contributes $15$ percent of an employee's salary to a retirement account for the employee up to the amount limited by the tax law. Because it provides the money purchase pension plan, SV does not contribute to the employee's $401($k$)$ plan. Matthew would like to maximize his contribution to his $401($k$)$ account after SV$\text{'}$s contribution to the money purchase plan.

Assuming Matthew's annual salary is $$379,000,$

Required:

a$-1.$ What amount will SV contribute to Matthew's money purchase plan?

a$-2.$ What can Matthew contribute to his $401($k$)$ account in $2023?$

Assuming Matthew's annual salary is $$246,300,$

Required:

b$-1.$ What amount will SV contribute to Matthew's money purchase plan?

b$-2.$ What can Matthew contribute to his $401($k$)$ account in $2023?$

Assuming Matthew's annual salary is $$58,900,$

Required:

c$-1.$ What amount will SV contribute to Matthew's money purchase plan?

c$-2.$ What amount can Matthew contribute to his $401($k$)$ account in $2023?$

d$.$ Assume Matthew's annual salary is $$58,900$ and that he is $54$ years old at the end of $2023.$ What amount can Matthew contribute to his $401($k$)$ account in $2023?$