An investor buys two 20-year bonds each having semiannual coupons and each maturing at par. For each bond the purchase price produces the same yield rate to maturity. One bond has a par value of $500 and a coupon of $45; the other bond has a par value of $1,000 and a coupon of $30. The dollar amount of premium on the first bond is twice as great as the dollar amount of discount on the second bond. What yield rate, convertible semiannually, does the investor realize? (Answer to the nearest 0.1%)

3. saving two consumers, larry and jeff, have utility functions defined over the two periods of their lives: middle age (period zero) and retirement (period 1). they have the same income in period 0 of m dollars and they will not earn income in period 1. the interest rate they face is r. larry’s and jeff’s utility functions are as follow. = 0.5 + 0.5 and = 0.5 + 0.5 for each person is between zero and one and represents each consumer’s temporal discount econ 340: intermediate microeconomics. ben van kammen: purdue university. rate. a. write the budget constraint that applies to both jeff and larry in terms of consumption in each period and ), interest rate, and m. b. what is larry’s and what is jeff’s marginal rate of intertemporal substitution? c. what is the slope of the budget constraint? d. write each consumer’s condition for lifetime utility maximization. e. re-arrange the conditions from part (d) to solve for the ratio, . f. if > which consumer will save more of his middle age income? g. if > 1 1+ , in which period will larry consume more: = 0 or = 1?