Computation of Periodic (Effective) Monthly Rate:

Periodic (Effective) Annual Rate = (1+i/n)^n - 1

Here,

Stated interest Rate (APR) = 3.84% 

n = Number of Compounding Periods = 12 

Periodic (Effective) Annual Rate = (1+3.84%/12)^12 - 1 = 1.039083 - 1 = 0.039083 or 3.91%

Periodic (Effective) Monthly Rate = 3.91%/12 = 0.326%

Computation of Borrowed Amount using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Borrowed Amount = ?

Rate =  3.84%/12

Nper = 30 years * 12 months = 360 months 

PMT = $3,800

FV = 0

Substituting the values in formula:

=-pv(3.84%/12,360,3800,0)

PV or Borrowed Amount = $811,554.26