Question

Find the present value of payments of $250 every six months starting immediately and continuing through 6 years from the present, and $150 every six months thereafter through 15 years from the present. if i(2) = 5.5%.

Answer 1

PV = PVA($250) + PV[PVA($150)]

1st Annuity: $250 every 6 months

PVA($250) = Annuity x [{1 - (1 + r)^-n} / r]

= $250 x [{1 - (1 + 0.055/2)^-(6*2)} / (0.055/2)]

= $250 x [0.2779 / 0.0275] = $250 x 10.1042 = $2,526.050915

2nd Annuity: $150 every 6 months

PVA($250) = Annuity x [{1 - (1 + r)^-n} / r]

= $150 x [{1 - (1 + 0.055/2)^-(15*2)} / (0.055/2)]

= $150 x [0.5569 / 0.0275] = $150 x 20.2493 = $3,037.40

PV[PVA($250)] = PVA($250)/(1 + r)ⁿ

= $3,037.40 / 1.055⁶ = $3,037.40 / 1.3788 = $2,202.86

Hence,

Total PV = $2,526.05 + $2,202.86 = $4,728.91