Computation of the present value of annuity:-

Correct option is B). $3,985

PV of annuity = Annuity*((1-1/(1+rate)^n)/rate)

Here,

Rate 2.27% (quarterly)

n = 5*4 = 20 periods (quarterly)

PV of annuity = $250*((1-1/(1+2.27%)^20)/2.27%)

= $250*15.93796

= $3,984.50 Or $3,985

 

Working note:-

EAR = (1+APR/n)^n-1

= (1+9%/12)^12-1

= 1.0938 - 1

= 9.38%

EAR = (1+APR/n)^n-1

9.38% = (1+APR/4)^4-1

(1+APR/4) = (1+9.38%)^(1/4)

APR/4 = 1.0227 - 1

APR = 2.27% * 4

= 9.07%