Dear,tutor,I want you to help in my last question,jot down at end

Subject:FinancePrice:2.86 Bought7

Share With

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.

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?