An annuity makes seven annual payments of $10,000 each, with the first payment occurring five years from today. lf the discount rate is 6% per year, thevalue of theannuity today is closest to:
$41,715.
$44.218
$55,824
B. Correct because the present value in Year 4of an ordinary annuity with 7 payments of $10,000 at a 6% discount rate is calculated as follows: PV=A[1-1/(1 + rN/rPV4= $10,000 x[1-1/(1 + 0.06)7]/0.06 PV4= $55,823.81 Then, using a timeline, the PV of the annuity in today's dollars is PVo = FV (1 + r)-N PVo = $55,823.81 x (1 + 0.06)-4PV,= $44,217.69 ≈ $44,218.
Calculator solution: (1)END mode; N = 7;1= 6; PMT = -10,000; FV = 0;solve for PV = 55,823.81.(2)END mode; N = 4;1= 6; PMT = 0; FV = -55,823.81; solve for PV =44,217.69.
