Adam is going to invest in an account paying an interest rate of $4.2 \%$ compounded quarterly. How much would Adam need to invest, to the nearest dollar, for the value of the account to reach $\$ 6,200$ in 19 years?

Step 1 ：Given that the final amount (A) is $6200, the annual interest rate (r) is 4.2% or 0.042 in decimal, the number of times the interest is compounded per year (n) is 4 (quarterly), and the time the money is invested for (t) is 19 years.

Step 2 ：We need to find the principal amount (P), which is the initial amount Adam needs to invest. We can use the formula for compound interest, rearranged to solve for P: \(P = \frac{A}{(1 + \frac{r}{n})^{nt}}\)

Step 3 ：Substituting the given values into the formula, we get: \(P = \frac{6200}{(1 + \frac{0.042}{4})^{4*19}}\)

Step 4 ：Solving the equation gives us the value of P.

Step 5 ：Final Answer: Adam would need to invest approximately \(\boxed{2803}\) for the value of the account to reach $6200 in 19 years.