Can please someone solve to me these questions, I will rate the answer if it is
ID: 2733448 • Letter: C
Question
Can please someone solve to me these questions, I will rate the answer if it is clear and laws used are 100% correct. Thanks and sorry for inconvenience.
1. A $ 1,000 , 10% semiannual bond is purchased for $ 1,010 . If the bond is sold at the end of year 3 , what would be the selling price to yield a 10% return on the investment??
2. The selling price of a $ 10,000 , 10% bond is $ 12,000 . If the bond pays interest semiannually and will mature in 20 years , Find the current yield and the yield to maturity.Assume that interest is compounded annually.
Explanation / Answer
1. Present value of bond = interest × pvaf + maturity value ×pvf
In case of semiannual bond , interest and discount rate is halved while time is doubled.
In the given question,
Interest = 10% /2 = 5% , Ytm = 10/2 = 5% , time = 3 × 2 = 6 period
Pvaf ( cumulative) = 1/(1+.05)6 = 5.075
Pvf = 1/(1.05)6 = .746
Present value of bond =1000 × 5% × 5.0756 +1000 ×.746
=$999.78 or $1000 approx
2. Current yield = semiannual interest ×100 / current price of bond
= 10000× 10% × 100/ 12000 = 8.333% per annum or 4. 1667 % semiannual
Yield to maturity in case of semiannual = interest half yearly+ (current price - maturity value)/life of bond ×2
/ (current price + maturity value )/2
= 500 + (12000 -10000)/( 20 × 2) / (12000 +10000)2
= 500+ (2000 /40 ) / 11000
= (500 + 50 ) ×100/ 11000
= 5% semiannual