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:

Mrs. Johnson is somewhat uncertain how long she will stay in London. She is considering moving move outside of the city in 10 years.

a. Calculate how much her investment would have grown to if she chooses option 1

b. If she chooses option 2, she believes that she would be able to sell the apartment after 10 years and have 250,000 left after paying the rest of her loan back

c. Which option is best with 10-year horizon?

FOR YOUR INFORMATION:

The question is related to following concepts:

1. characteristics of an annuit
2. perpetuity
3. FV of an immediate ordinary annuity
4. PV of a growing perpetuity