Problem 1 (14 points): Consider the following information about four bonds and assume they are priced correctly: Bond #1 Time to maturity 0.5 Coupon rate 5% Bond #2 1 9% Bond #3 Bond #4 20 20 8% 4% Price 100.59 104.76 123.11 80.89 a) (2 points) Find a 6-month spot interest rate. Keep at least 6 decimal digits while performing your calculations b) (2 points) Find a 1-year forward interest rate. Keep at least 6 decimal digits while performing your calculations c) (2 points) Find a 1-year spot interest rate. Keep at least 6 decimal digits while performing your calculations d) (2 points) Find a 20-year spot interest rate. Keep at least 6 decimal digits while performing your calculations. e) (3 points) Find the price of a 20-year 2% coupon bond. Keep at least 6 decimal digits while performing your calculations f) (3 points) Find the price of a perpetuity that pays you $2 every six months (with the first payment 6 months from now) if all forward interest rates from year 20 to infinity are 6% (note: you cannot assume that all forward rates from now till infinity are 6%)