Question

Suppose the one year spot rate and two year spot rate are both 3%. a) What...

Suppose the one year spot rate and two year spot rate are both 3%.

a) What is the price of a two year ZCB?
b) What is the price of a one year ZCB today?
c) What do I expect the price of a one year ZCB to be, one year from now?

Same 3 questions except now the one year spot rate is 3% and the 2 year spot rate is 4%.

Same 3 questions except now the one year spot rate is 3% and the 2 year spot rate is 2%.

ZCB-zero coupon bond

explain in full detail with correct formulas

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Answer #1

Zero Coupon Bond Price = F / (1 + i)^n

where:

F = face value or maturity value = 100 (Assuming bond will mature at $100. This assumption is based on the historical data as Zero coupon bonds usually have maturity value $100, $1000 and so on)

i = interest rate = 3%

n = maturity period = 1 year and 2 year

a) What is the price of a two year ZCB?

Price = 100 / (1 + 0.03)^2 = 94.26 (Rounded off to two decimal )

b) What is the price of a one year ZCB today?

Price = 100 / (1 + 0.03) = 97.09 (Rounded off to two decimal)

c) What do I expect the price of a one year ZCB to be, one year from now?

It would be $100 as ZCB is maturing after one year from now and maturity price is 100

Same 3 questions except now the one year spot rate is 3% and the 2 year spot rate is 4%.

a) What is the price of a two year ZCB?

Price = 100 / (1 + 0.04)^2 = 92.46 (Rounded off to two decimal )

b) What is the price of a one year ZCB today?

Price = 100 / (1 + 0.03) = 97.09 (Rounded off to two decimal)

) What do I expect the price of a one year ZCB to be, one year from now?

It would be $100 as ZCB is maturing after one year from now and maturity price is 100

Same 3 questions except now the one year spot rate is 3% and the 2 year spot rate is 2%.

a) What is the price of a two year ZCB?

Price = 100 / (1 + 0.02)^2 = 96.12 (Rounded off to two decimal )

b) What is the price of a one year ZCB today?

Price = 100 / (1 + 0.03) = 97.09 (Rounded off to two decimal)

) What do I expect the price of a one year ZCB to be, one year from now?

It would be $100 as ZCB is maturing after one year from now and maturity price is 100

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