1. Price a 2% coupon, $1,000 face value 10 year bond if market rates are 4% for the first 5 years and 5% for the last 5 years. Show in dollars and percent what you earn if you hold this bond for 2 years.
2. Price a stock that pays a $3/year dividend for the next 10 years. After which it pays a $1/year dividend forever given a discount rate of 10%. Show in dollars and percent that you earn if you hold this stock for three years.
3. Your brother-in-law needs a loan again. This time he needs to borrow $10,000. He always comes to you because you only charge him 4% interest per year. He promises to pay you $2,000 a year from now, $4,000 in two years and the rest of what he owes you in three years. How much will his third payment be? Suppose at the end of year three he says, “well, I’ve paid you $6,000, what’s left must be $4,000”. Explain to him intuitively why that’s not, in fact, what he owes you.