#### Explanation:

Amounts the person in question deposits each year

• $color(white)(l) 200 in the first $1 \text{st}$year, • (1+15%) xx$ color(white)(l) 200 in the second $2 \text{nd}$ year,
• (1+15%)^2 xx $color(white)(l) 200 in the third $3 \text{rd}$year, • $\cdot \cdot \cdot$• (1+15%)^19 xx$ color(white)(l) 200 in the twentieth $20 \text{th}$ year,

form a geometric sequence.

A general formula gives the sum of the first $n \text{th}$ terms of a geometric sequence of common ratio $r$ and first term ${a}_{1}$

${\sum}_{i = 1}^{n} {r}^{i - 1} \times {a}_{1} = {a}_{1} \times \frac{1 - {r}^{n}}{1 - r}$

The geometric sequence in this question has

r = 1+15% = 1.15

as its common ratio and

a_1=$color(white)(l) 200 as the first term, which equals to the deposit in the very first year. The question is asking for the sum of the first twentieth terms of this sequence, implying $n = 20$; substituting $n$, $r$, and ${a}_{1}$with their respective values and evaluating the summation gives sum_(i=1)^(20) 1.15^(i-1) xx$ color(white)(l) 200 = $color(white)(l) 200 xx (1-1.15^20)/(1-1.15) =$ color(white)(l) 20488.72
(rounded to the two decimal places)

Therefore the person would have deposited  \$ color(white)(l) 20488.72 in total in the twenty years.