Problem [i] An investment that requires $1,000 initial investment will return $600 at the end of first year and $650 at the end of second year. Assume the discount rate is continuously compounded at 8%. What is the Net Present Value of the investment?

Problem [ii]

Suppose that the 6-month, 12-month, 18-month, 24-month, and 30-month zero rates continuously compounded are 4%, 4,2%, 4.4%, 4.6%, and 4.8% per annum, respectively. What is the price of a bond with face value of 100 that will mature in 30 months pays a coupon of 4% per annum semiannually?

Problem [iii]

Suppose that risk-free zero interest rates with continuous compounding are as follows:

Maturity( years)	Rate (% per annum)	Forward Rate
1	2.0
2	3.0	?
3	3.7	?
4	4.2	?
5	4.5	?

Calculate forward interest rates for the second, third, fourth, and fifth years.

Problem [iv]

Use the risk-free rates in the previous Problem. You are entering an FRA where you will pay 5% (annually compounded) for the third year and receive LIBOR on $1 million. The forward LIBOR rate (annually compounded) for the third year is 5.5%. What is the value of the FRA today?

PLEASE SHOW ALL WORK!