Calculate the amount that must be invested at the end of each year at $10\mathrm{.}4\%$ compounded annually in order to accumulate $$640,000$ after: $($Do not round intermediate calculations and round your final answers to $2$ decimal places.$)$

a$.35$ years.

b$.40$ years.

In each case, also determine what portion of the $$640,000$ represents earnings on the annual investments. $($Round your intermediate calculations and final answers to $2$ decimal places.$)$

a$.$ Earnings portion

b$.$ Earnings portion