Consider a bond that pays no face value at the end of its life. It only pays growing coupons every year, at a growing rate of 5% each year. This security lasts for 4 years (i.e., makes 4 payments). The current annual interest rate is 5% for all maturities.

1. What is the price of this bond today?

2. What is the duration of this bond today?

3. Find the coupon rate of another bond that has the same price of this bond, but a growth rate of the coupons of 10%.

4. Calculate the duration of the new bond. How does it compare to the duration of the previous bond? Discuss.