Answer
The money deposited on the $21^{st}$ birthday is $\$1250$.
The total amount deposited over the 21 years is $\$15,750$.
Work Step by Step
The situation can be modeled by an arithmetic sequence, with $a_{1} = 250$ and $d = 50$, which the general term is $a_{n} = 250 + (n-1)(50)$ where n is the number of years.
The money deposited on the $21^{st}$ birthday (n = 21) is
$a_{21} = 250 + (21-1)(50)$ = $\$1250$
And, the total amount deposited over the 21 years is
$\sum\limits_{n=1}^{21} a_{n} = \sum\limits_{n=1}^{21} [250 + (n-1)(50)]$
= $\frac{21(250 + 1250)}{2}$
= $\$15,750$
