Computation of Amount She will have in the account at the End of Fourth Year:

Future value of Annuity = P (((1+r)ⁿ -1)/r)

Here,

P = Periodic Payment = $1,000 per quarter

r = Interest Rate = 12%/4 = 3% per quarter

n = Number of Compounding Periods = 4 years*4 quarters = 16

Future value of Annuity = 1000*((((1+0.03)^16 -1)/0.03)

= 1000*20.15688

Future value of Annuity = $20,156.88 or $20,157

So, Amount She will have in the account at the End of Fourth Year is $20,157.