Dear tutor,

I want you to help in my last question,jot down at end.I have learned the questions but adding their solutions because I believe the last question is subsequent to these questions and would help you in understanding my question(last one) easily.I would be glad if you can help me out.

The Scenario is:

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

QUESTIONS:

Q1. In case Mrs. Johnson chooses option 2, how much will she have to pay each month for her loan?

Her payment each month can be calculated using the PMT function of excel or financial calculator. Inputs are:

Rate = interest rate per month = 1.5% / 12 = 0.125%

Nper = number of months in years to maturity = 12 x 30 = 360

PV = - Loan amount = - 800,000

FV = future value = 0

Hence, the amount she will have to pay each month for her loan

= PMT (Rate, Nper, PV, FV) = PMT (0.125%, 360, - 800000, 0) = 2,760.96

Q2. 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.

Monthly rent in year n = Monthly rent in year (n-1) x (1 + annual increase) = Monthly rate in year (n-1) x (1 + 2.5%)

Monthly rent in year 1 = 2,000

Hence, we can construct the following table of year wise monthly rent as shown below:

Year	Monthly rent
1	2,000
2	2,050
3	2,101
4	2,154
5	2,208
6	2,263
7	2,319
8	2,377
9	2,437
10	2,498

Q3. How much rent would she have paid in total over the 10 years?

Rent paid for the first year = 2,000 x 12 = 24,000 Rent paid for the second year = 2,000 x 1.025 x 12 = 24,600 Rent paid for the third year = 2,000 x 1.025² x 12 = 25,215 Rent paid for the fourth year = 2,000 x 1.025³ x 12 = 25,845 Rent paid for the fifth year = 2,000 x 1.025⁴ x 12 = 26,492 Rent paid for the sixth year = 2,000 x 1.025⁵ x 12 = 27,154 Rent paid for the seventh year = 2,000 x 1.025⁶ x 12 = 27,833 Rent paid for the eighth year = 2,000 x 1.025⁷ x 12 = 28,528 Rent paid for the ninth year = 2,000 x 1.025⁸ x 12 = 29,242 Rent paid for the tenth year = 2,000 x 1.025⁹ x 12 = 29,973

Total rent paid = sum of all the above rents = 268,882

Q4. If she chooses option 1, she believes she can invest 100,000 today and in addition, 600 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?

Initial Investment PV = 100,000 Monthly investment P = 600 Monthly rate - 6 / 12 = 0.5% Number of months = 30 x 12 = 360

Future value of the investements = FV of the Monthly investmetns + FV of the Intial investment FV = P x [(1 + r)ⁿ - 1] / r + FV x (1 + r)ⁿ = 600 x [(1 + 0.005)³⁶⁰ - 1] / 0.005 + 100,000 x (1 + 0.005)³⁶⁰ = 602,709 + 602,258 = 1,204,967

Q5. 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 1,200,000 in 30 years at which point she will have no debt. Which options provides the largest savings after 30 years?

In Option 1 you will have 1,204,967 at the end of 30 years. Whereas in option 2, you invest in apartment today which will have net value of 1,200,000 at the end of 30 years.

Since value of investment at end of 30 years is more in option 1 (1,204,967) is than in option 2 (1,200,000).

Option 1 provides the largest savings after 30 years.

Dear Tutor,I need your help in following question:

QUESTION:

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?