Consider Country (Z) with a GDP level of 210,000 and a growth rate of 5% in 2019 (i. e. calculated at the end of year 2019). The experts predict that the growth of the economy of Country (Z) wills gradually slowdown in the coming years. More precisely, they foresee the following growth rates for the future: 2019 – 2022 (5%), 2022 – 2025 (3%). Hint: The list above should be read as saying that, for instance, `the growth rate from the end of 2019 until the end of 2022 will be 5%, then from the end of 2022 until the end of 2025 it will be 3%’ and so on. Requirement a) Assuming that the predictions of the experts listed above are accurate, when in the future will Country Z’s GDP double compared to the GDP level of 2019? [10 marks] b) What would Country Z’s GDP growth rate be from 2025 and so on at 1%? Explain your reasoning carefully. [5 marks] c) Consider now the more optimistic scenario in which the economy does not slow down and the current growth rate of 5% remains constant in the coming years. How long will it take for the GDP level to double in this scenario? Express your answer in two forms: i) In number of years [5 marks] ii) As a fraction of your answer in part a.

Onsider the following subscription behavior information from genie, a web site that provides tools for constructing a family tree (ancestor search). subscriptions cost $9.99 per month, but you are charged for the entire year at the time of purchase. there is a one-year minimum term when you sign up for the service. once purchased, subscriptions are set to renew automatically unless the subscriber cancels them. when a membership renews, it renews for a one-year term and again you are charged for the entire year. there are no variable costs associated with providing this service to an individual customer, but genie does engage in customer relationship activities that they believe will increase customer retention. these customer relationship activities cost genie about $10 per year per customer. based on a sample of 1000 customers that joined genie five years ago, near the time when the company was founded, they were able to determine how many of those customers remained subscribers in the second year, third year etc. based on this information, genie calculated the average annual retention rate to be 20%. genie uses an annual discount rate of 8%. a. last year, genie spent $10,000 placing advertisements on google. genie management believes that these advertisements were responsible for about 300 new subscribers. would you recommend to genie management that they purchase more google ads? b. suppose a newly-introduced loyalty program increases the number of customers that remained to 30%. does this new data change your answer to 9.a? c. do you have any hesitations or concerns about making recommendations to management based on your above estimate of customer lifetime value?