Question 3. (27 points) (a) Suppose that an investment account increases in value at a rate r1 in 6 months and then decreases in value by r2 over the next six months. Give the formula for the annual growth factor on this account.

(b) If r1 = r2 > 0 in part (a), what is the formula for the annual growth factor of this account?

(c) Is the growth factor in (b) less than, equal to or greater than 1? (Circle your answer).

(d) If the account decreases by 20% in the first 6 months, what percentage increase is needed in the second 6 months, to avoid having a loss for the year?

(e) A zero coupon bond has 3 years to maturity and may be bought for $94. Give the formula for the annual discount rate on this bond. Is the internal rate of return on this bound less than, equal to or greater than 2%? (Circle your answer).