Find the final amount in the following retirement account, in which the rate of return on the account and the regular contribution change over time.

$$350$ per month invested at $5\%,$ compounded monthly, for $7$ years; then $$471$ per month invested at $6\%,$ compounded monthly, for $7$ years.

What is the amount in the account after $14$ years?

$ $($Do not round until the final answer. Then round to the nearest dollar as needed.$)$