A loan is taken to purchase experimental supplies for development of a personal device that can be used to obtain clean water from many common contaminated sources. The loan is for $190,000 and is to be paid back in equal annual amounts over a period of 4 years at an annual rate of 7%.

Another possibility is to pay $22,000 in year 1, followed by a geometrically increasing series of amounts in years 2, 3, and 4. What is the geometric rate of increase in percent that makes this option equivalent to the equal annual amount?

Please show work.