Question

Consider the following bond purchased at $800 in 2018. F=1000; C=100; N=5; P=800 If the investor sold the bond in 2019 without holding till maturity did he/she make a profit or a loss? What is the rate of return in 2019?

Answer 1

Given Face value F=$1000

and price of bond B=$800 Eq 1

C=$100

N=5

Let r be the interest rate

So B=C*(1-(1+r)^-N)/r + F/(1+r)^N

800=100*(1-(1+r)^-5)/r + 1000/(1+r)^5

so solving for r we get

r=16.13%

So bond price in 2019 will be

B=C*(1-(1+r)^-(N-1))/r + F/(1+r)^(N-1)

B=100*(1-(1+16.13%)^4)/16.13%+ 1000/(1+16.13%)^4

B=$829 eq 2

So from equation 1 and 2 we find that we investor sell the bond in 2019 then he will make profit.

Total Profit = Selling price + coupon - purchase price = 829+100-800=$129

rate of return =129/800=16.13%