Answer:
Current Price of Bond M is $28,406.72
Current Price of Bond N is $2,840.91
Explanation:
BOND M
PV of par paid at maturity is:
= Face Value / (1 + r) ^ n
where
r is rate which is 5% because it is semiannually so, in this the rate will be:
= 10 / 2
= 5%
n is number of years which is 40 because it is semiannually, so the number of years got doubled
= 20,000 / (1+ 0.05) ^ 40
= $2,840.92
PV of the 16 will be computed by using the Present Value annuity:
PVOA = PMT [ (1 - {1/ (1 + i) ^ n}) / i ]
where
Pmt is $3,000
n is 16 years
i is 0.05
= 3,000 [ (1 - {1/ (1 + 0.05) ^ 16}) / 0.05]
= 3,000 [ (1- 0.45811) / 0.05]
= 3,000 × 10.8378
= $32,513.4
PV at t = 0
= 32,513.4 / 1.05 ^ 12
= $18,104.68
PV of the 12 year
where
pmt is $3,300
t =14
= 3300 [ ( 1- {1/ 1.05 ^12)} / 0.05]
= 3300 [ 0.44316 / 0.05]
= $29,248.56
PV at 12
= 29,248.56 / 1.05 ^12
= $7,461.12
PV of Bond M = $2,840.92 + $18,104.68 + $7,461.12
= $28,406.72
BOND N
The Present value of Bond N is computed by using the excel formula of present value:
=-PV(rate,nper,pmt,fv, type)
where
rate is 5%
nper is 40 because it is semiannually, so the number of years got doubled
pmt is 0
Fv is $20,000
Putting the values in the formula:
=-Pv(5%,40,0,20000,0)
= $2,840.91
