On january 1, 1980, moises deposited $1850 into a savings account paying 5.6% interest, compounded quarterly. if he hasn't made any additional deposits or withdrawals since then, and if the interest rate has stayed the same, in what year did his balance hit $3700, according to the rule of 72?

We first calculate for the effective interest of the given nominal interest that is compounded quarterly through the equation,
                           ieff = (1 + i/4)^4 - 1
Substituting the known values,
                           ieff = (1 + 0.056/4)^4 -1 = 0.05718

To determine the future worth of a money invested with an interest that is compounded, the equation is,
                             F = P x (1 + ieff)^n
where P is the present worth and n is the number of years. 

For this item, we substitute the known terms in the derived second equation
                       3700 = (1850) x (1 + 0.05718)^n
The value of n is 12.46 years. 

Therefore, the money will be worth $3700 only on 1992.