Please help me in answering my question:

Mrs. Johnson has just moved to London with her new job, in which she received a significant salary increase. Being new to the city, she is now trying to decide whether she should rent an apartment or buy one. She has spent the first weekend looking at different options and has shortlisted two options.

Option 1: Rent an apartment, which would cost her a total of 2,000 per month including everything. Every year the rent is due to increase by 2.5%. The contract is perpetual meaning she could theoretically stay there forever if she wanted.

Option 2: Buy an apartment, which costs 900,000 with an initial down payment of 100,000 and a 30-year loan for the remaining 800,000. The loan would carry an interest of 1.5%. After 30 years she would own the apartment 100% .

Assumptions

1. She will buy or rent the apartment on the 1st of January

2. Payments happen at the end of each period

Question.1

a.If she chooses option 2, she will not be able to invest anything (other than what she invests in her apartment). She believes that the apartment will be worth approximately 1,200,000 in 30 years at which point she will have no debt. Which options provides the largest savings after 30 years?

b. Upon retirement she expects to have a yearly cost of living of 25,000 in year one, which will increase each year by 3.5%. She believes she can continue to grow her investments at an annual return of 5.5%. As she does not know how old she will grow, she would like to assume that she needs payments in perpetuity to never run out of money. Will the two options allow her to live this way?