Question

The one-year continuously-compounded zero rate is 3.5% per annum. The two-year zero rate is 5% per annum. What is the forward rate for the second year?

4.25% per annum.

6.5% per annum.

7.5% per annum.

8.5% per annum.

If the continuously compounded interest rate is 12% per annum, what is the price of a two-year zero-coupon treasury bill with a face value of $100?

$76.0

$78.66

79.72

$80.64

The price of a two-year zero coupon bond with a face value of $1000 is trading at a price of $935. What is the annualized continuously-compounded yield of this bond?

3.36%

3.42%

6.72%

6.95%

Answer 1

Question 1) Option B:6.5% per annum

Given

One year rate R1=3.5%

Two year rate R2=5%

Let F be the forward rate

Since compounding is done continuously

So e^(R1)*e^(F)=e^(2*R2)

e^(3.5%)*e^(F)=e^(2*5%)

e^F=1.06716

F=6.5%

Question 2) Option B:$78.66

Continuous compounding interest rate r=12%

Two year zero coupon bond with face value F=$100

Let P is the price of Bond

F=P*e^(2*r)

100=P*e^(2*12%)

P=100/1.2712=$78.66

Question 3) Option A:3.36%

Given

Price of two years zero coupon Bond P=$935

Face value F=$1000

Let r be the annualized rate continuous compounding

So F=P*e^(2r)

1000=935*e^(2r)

e^(2r)=1.0695

r=0.0336=3.36%