1) A $21,000, 9

1) Computation of the purchase price of the bond:-

Purchase price of bond = (C*((1-1/(1+rate)^n)/rate))+(FV/(1+rate)^n)

Here,

Coupon payment = $21,000*9.5%/2 = $997.50

Rate = 8.2%/2 = 4.1% (semiannual)

n = 12*2 = 24 periods (semiannual)

Purchase price of bond = ($997.50*((1-1/(1+4.1%)^24)/4.1%))+($21,000/(1+4.1%)^24)

= ($997.50*15.092049) + ($21,000/2.623116)

= $15,054.319097 + $8,005.745621

= $23,060.06

2) Computation of the purchase price of property:-

First we calculate the present value of annuity ;

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

Here, rate = 6.14% / 2 = 3.07% (semiannual)

n = 10*2 20 periods (semiannual)

PV of annuity = $867*((1-1/(1+3.07%)^20)/3.07%

= $867*14.7841

= $12,817.84

Purchase price = Down payment + PV of annuity

= $7,640 + $12,817.84

= $20,457.84

Working note:-

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

= (1+6%/4)^4-1

= 1.0614 - 1

= 6.14%

Computation of the cost of financing:-

Cost of financing = Total payment - PV of annuity

= ($867*10*2) - $12,817.84

= $17,340 - $12,817.84

= $4,522.16