Problem Set 3 (Due Feb 13)

1. Three years ago you took out a 30-year amortizing loan. The loan has a 6%

APR with monthly payments (and monthly compounding).

a) (5 points) What are your monthly payments if your current loan balance

is $368; 600?

b) (5 points) How much interest did you pay on the loan in the past year?

2.

On 1/1/10, the following is observed for grade AAA (risk-free)

bonds:

- A bond maturing on 12/31/12 with coupon 6.0% and face value $1000 is

selling at $1112.80

- A bond maturing on 12/31/12 with coupon 5.0% and face value $1000 is

selling at $1084.00

- A T-bill maturing on 12/31/10 is quoted with a yield to maturity of

2.0408%.

Assume that bond coupons are paid annually on 12/31.

a) (3 point) Find the price as of 1/1/10 of $1 delivered in one year (p1 ).

b) (3 points) Find the prices as of 1/1/10 of $1 delivered in two years and

three years (p2 and p3 ). (HINT: You may need to solve a system of equations)

c) (3 point) Write down the cash ows of a three-year risk-free bond that

has face value of $1,000 and pays coupon C each year-end.

d) (3 points) What is the coupon rate (coupon divided by face value) which

must be paid for a newly-issued (on 1/1/10) three-year risk-free bond with face

value of $1000 to sell at par? (sell at Par means market value = face (or

principal) value.) Use your prices from a) and b).

e) (3 points) What is the coupon rate which must be paid for a newly-issued

(on 1/1/10) two-year risk-free bond to sell at par?