You are asked to answer all the questions in the proposed case.

Task 3.1 Concepts 1. State the characteristics of an annuity

2. How does a perpetuity differ from an annuity?

Task 3.2 Formulas

3. State the formula for the FV of an immediate ordinary annuity

4. State the formula for the PV of a growing perpetuity

Task 3. 3

Annuity & Perpetuity calculations

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 3,000 per month including everything. Every year the rent is due to increase by 2.50%. The contract is perpetual meaning she could theoretically stay there forever if she wanted.

Option 2: Buy an apartment, which costs 1,350,000 with an initial down payment of 150,000 and a 30-year loan for the remaining 1,200,000. 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

Questions 1. In case Mrs. Johnson chooses option 2, how much will she have to pay each month for her loan?

2. In option 1, Mrs. Johnson is unsure how much rent she will have to pay in the future. Show the monthly rent per year from year 1-10

3. How much rent would she have paid in total over the 10 years?

4. If she chooses option 1, she believes she can invest 150,000 today and in addition, 900 each month in a financial product that offers 6% return. Assuming she plans to retire in 30 years, how much will she have saved up?

5. Alternatively, 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 1,800,000 in 30 years at which point she will have no debt. Which options provides the largest savings after 30 years?

6. Upon retirement she expects to have a yearly cost of living of 37,500 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?

7. 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 375,000 left after paying the rest of her loan back

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