Question

A bond currently promises annual payments of $1000 per year for 5 years. In addition, the bond will make an additional single payment on maturity (in the fifth year) of $10,000.

(a) If the interest rate on similar investments is currently 5% (i=.05) what will be the price of this bond? Explain and show your calculations. (b) What happens to the price if the interest rate on similar investments falls to 4%? Show your work.

Answer 1

a)

Annual payment=R=$1000

Number of annual payments=n=5

Maturity amount=FV=$10000

Discount rate=i=5%

Price of bond should be equal to present value of future payments.

Price=R*(P/A,0.05,5)+FV*(P/F,0.05,5)=1000*(P/A,0.05,5)+10000*(P/F,0.05,5)

Let us calculate the interest factors

(P/F,0.05,5)=1/(1+0.05)^5=0.783526

So,

Price=1000*4.329477+10000*0.783526=$12164.74

b)

Discount rate=i=4%

Price=R*(P/A,0.04,5)+FV*(P/F,0.04,5)=1000*(P/A,0.04,5)+10000*(P/F,0.04,5)

Let us calculate the interest factors

(P/F,0.04,5)=1/(1+0.04)^5=0.821927

So,

Price=1000*4.451822+10000*0.821927=$12671.09

Price will increase to $12671.09