Answer:
a: current value of the bond $405.11
b: Robison loss: 59.49%
c Pinson gain: 146.85%
As the investment is smaller the percentage change at maturity is greater than the difference in percentage of the par value.
A percent of the original investmentrepresent 10 dollars while !% of Mrs Pinson represent 4.05 dollars
Explanation:
The present value of the bonds is the sum of the present value of the coupon payment and the maturity discounted at market rate:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C: 1,000 x 8% / 2 = 40.00
time: 25 years x 2 payment per year = 50
market rate 0.10
[tex]40 \times \frac{1-(1+0.1)^{-50} }{0.1} = PV\\[/tex]
PV $396.5926
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 50.00
rate 0.1
[tex]\frac{1000}{(1 + 0.1)^{50} } = PV[/tex]
PV 8.52
PV c $396.5926
PV m $8.5186
Total $405.1111
Robinson capital loss:
405.1111/ 1,000 -1 = -59.49%
If purchased today and held to maturity by Mrs Pinson:
1,000 / 405.1111 - 1 = 146.85%
