1) A one year zero coupon bond (ZCB) with face value $100 is priced as $99.

A two year ZCB with face value $100 is priced as $98.A third bond matures in two years, its face value is $1000, It pays fixed $5 coupon annually. The next coupon is in one year.

What is the price of the third bond?

Round your answer to the cent, e.g. $1000.345 should be entered as "1000.35",

A hint: use prices of ZCBs to determine discount factors.

2) A one year spot rate is 1%.

A two year spot rate is 3%.

A bond matures in two years, its face value is $1000, It pays fixed $5 coupon annually. The next coupon is in one year.

What is the price of the bond?

Round your answer to the cent, e.g. $1000.345 should be entered as "1000.35",

A hint: use spot rates to calculate discount factors of cash flows.

3)

A two year zero coupon bond with face value $1000 is priced at $960.

Calculate its effective duration using a small step of 1 basis point, i.e. 0.01%, and finite differences approximation of a derivative.

Round your answer to two decimal points, e.g. 23.3456 should be entered as "23.35",

A hint: calculate the yield to maturity first, which is a spot rate in this case.

4) A bond portfolio has effective duration 5 and convexity -23. The current market value of the portfolio is $100 Billion. Use Taylor approximation and Duration and Convexity to find what would be the market value of the portfolio if the spot yield curve experiences a parallel shift down by 10 basis points.

One basis point is 0.01%

Round your answer to millions, e.g. $9.98766 Billions should be entered as "9988",

5)Two year spot rate is 1.45%, three year spot rate is 1.39%. What is a one year forward rate two years from today, 2F1?

It is the rate to borrow two years later from today for one year.

Enter your answer in basis points, i.e. 1.45% would be entered as "145".

One basis point is 0.01%