Question

Suppose that you own a zero coupon bond that will mature in 10 years. The face value of the bond is $10,000.

a. If the (nominal) interest rate is currently 5% and is expected to remain at 5% for the life of the bond, what should the bond’s current price be?

b. Assuming that you are right about future interest rates, what should the bond’s price be in 5 years?

c. Suppose, instead, that the (nominal) interest rate is currently 5%, but is expected to fall to 3% after 2 years (and remain at 3% after that). What should the bond’s current price be?

d. Assuming that interest rates follow the expected pattern (i.e. – 5% per year for 2 years; then 3% per year), what should the bond’s price be in 5 years?

Answer 1

Face value, M = $ 10,000

Coupon, C = 0

A. Nominal interest rate, i= 5%

Maturity period, N = 10 years

The price of bond can be calculated using the following formula

P = M*(P/A,i%,N)

P = $ 10,000 * (P/F,5%,10)

Price of bond = $ 10,000*0.613913

Current price = $ 6,139.13

B. Interest rate = 5%

Time 5

Price of bond= $ 10,000*(P/F,5%,5)= $ 10,000*0.783526

Price of Bond = $ 7,835.26

C. First two years 5%

Next 8 years 3%

Price of bond = $10,000(P/F,5%,2)*(P/F,3%,8)

Price = $ 10,000 * 0.716017

Price of bond = $ 7,160.17

D. Price of bond = $ 10,000*(P/F,3%,5) = $ 10,000*0.862608

Price of bond = $ 8,626.08

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