$1\mathrm{.}6\mathrm{.}12$ On January $1$ Smith deposits $1000$ into an account earning i$4)=08$

with interest credited on the last day of March, June, September, andDecember.

If Smith closes the account during the year, simple interest is paid on thebalance

from the most recent interest credit date.

$($a$)$ What is Smith's close$-$out balance on July $19?$

$($b$)$ Suppose all four quarters in the year are considered equal, and timeis

Derive expressions for Smith's accumulatedamountmeasured in years.

function A$($t$),$ the close$-$out balance at time t$.$ Consider separately thefour

intervals $0<$ t$<\mathrm{.}25,\mathrm{.}25$