FINANCIAL MATHEMATICS & BUSINESS STATISTICS

Financial Mathematics & Business Statistics



Financial Mathematics & Business Statistics

Question 1

On the 5th of March 2009, the Bank of England (BoE) lowered its main interest rate to 0.5%, the lowest on record since the Bank has published rates in 1970, which still remains unchanged. As a consequence of this low level of rates, HSBC's Lifetime Tracker Standard mortgage rate stands at 4.99%. Jeff Green is about to buy a house in the countryside which costs £650,000 and is taking out a 25-year repayment mortgage for 75% of the acquisition value of the house. Jeff has asked you to assess his ability to pay, in case the BoE increases its interest rate, as his maximum monthly payment cannot exceed £3,200. You are required to: Calculate the monthly payment John will need to meet under current conditions.

Assess the effect on John's monthly payments for each quarter percentage point increase in the BoE rate, up to 4% and identify at which rate Jeff would no longer be able to make the monthly payment.

Determine the shortest length (to the nearest month) of mortgage Jeff could take out if he wanted his monthly payment to be exactly the maximum he could afford (based on current mortgage assumptions).

Solution

Part 1

 

 

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Scenario 5

 

 

 

 

 

 

 

 

 

Basic Arrangements:

 

Maximum monthly payment

3,200.00

3,200.00

3,200.00

3,200.00

3,200.00

 

Term in years

25

25

25

25

25

 

Interest Rates:

 

Initial rate

0.50%

0.50%

0.50%

0.50%

0.50%

 

 

1st rate change after start

2

2

2

2

2

 

New rate

3.50%

3.50%

3.50%

3.50%

3.50%

 

 

2nd rate change after first change

1.5

1.5

1.5

1.5

1.5

 

New rate

4.00%

4.00%

4.00%

4.00%

4.00%

 

 

Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mortgage

714,072

714,072

714,072

714,072

714,072

 

Cost of borrowing

244,915

244,915

244,915

244,915

244,915

 

Payment Schedule:

 

Initial Stage:

1 at 0.50%

1 at 0.50%

1 at 0.50%

1 at 0.50%

1 at 0.50%

 

Monthly payment at initial interest rate

2,532.60

2,532.60

2,532.60

2,532.60

2,532.60

 

Interim Stage:

1 at 3.50%

1 at 3.50%

1 at 3.50%

1 at 3.50%

1 at 3.50%

 

Monthly payment after 1st rate change

2,854.74

2,854.74

2,854.74

2,854.74

2,854.74

 

Final Stage:

298 at 2.50%

298 at 2.50%

298 at 2.50%

298 at 2.50%

298 at 2.50%

 

Monthly payment after 2nd rate change

3,200.00

3,200.00

3,200.00

3,200.00

3,200.00

Part 2

 

Scenario 1

 

Scenario 2

 

Scenario 3

 

Scenario 4

 

Scenario 5

 

 

 

 

 

 

 

 

 

 

Basic Arrangements:

Mortgage

650,000

 

650,000

 

650,000

 

650,000

 

650,000

Term in years

25

 

25

 

25

 

25

 

25

Interest Rates:

Initial rate

0.50%

 

0.50%

 

0.50%

 

0.50%

 

0.50%

1st rate change after start

1

1

1

1

1

New rate

3.50%

 

3.50%

 

3.50%

 

3.50%

 

3.50%

2nd rate change after first change

1

 

1

 

1

 

1

 

1

New rate

4.50%

 

4.50%

 

4.50%

 

4.50%

 

4.50%

 

 

Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cost of borrowing

430,475

430,475

430,475

430,475

430,475

Payment Schedule:

Initial Stage:

1 at 0.50%

1 at 0.50%

1 at 0.50%

1 at 0.50%

1 at 0.50%

Monthly payment at initial interest rate

2,305.35

2,305.35

2,305.35

2,305.35

2,305.35

Interim Stage:

1 at 3.50%

1 at 3.50%

1 at 3.50%

1 at 3.50%

1 at 3.50%

Monthly payment after 1st rate change

3,250.66

3,250.66

3,250.66

3,250.66

3,250.66

Final Stage:

298 at 4.50%

298 at 4.50%

298 at 4.50%

298 at 4.50%

298 at 4.50%

Monthly payment after 2nd rate change

3,607.11

3,607.11

3,607.11

3,607.11

3,607.11

Outstanding debt at term end

0

0

0

0

0

 

 

 

 

 

 

 

 

 

 

 

Part 3

Basic Arrangements:

Maximum monthly payment

3,200.00

3,200.00

3,200.00

3,200.00

3,200.00

Term in years

25

25

25

25

25

Interest Rates:

Initial rate

0.50%

0.50%

0.50%

0.50%

0.50%

1st rate change after start

1

1

1

1

1

New rate

1.50%

1.50%

1.50%

1.50%

1.50%

2nd rate change after first change

3

 

3

 

3

 

3

 

3

New rate

4.50%

 

4.50%

 

4.50%

 

4.50%

 

4.50%

Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mortgage

578,113

578,113

578,113

578,113

578,113

Cost of borrowing

378,071

378,071

378,071

378,071

378,071

Payment Schedule:

Initial Stage:

1 at 0.50%

1 at 0.50%

1 at 0.50%

1 at 0.50%

1 at 0.50%

Monthly payment at initial interest rate

2,050.39

2,050.39

2,050.39

2,050.39

2,050.39

Interim Stage:

3 at 1.50%

3 at 1.50%

3 at 1.50%

3 at 1.50%

3 at 1.50%

Monthly payment after 1st rate change

2,311.20

2,311.20

2,311.20

2,311.20

2,311.20

Final Stage:

296 at 4.50%

296 at 4.50%

296 at 4.50%

296 at 4.50%

296 at 4.50%

Monthly payment after 2nd rate change

3,200.00

3,200.00

3,200.00

3,200.00

3,200.00

Question 2

A company that manufactures electrical appliances is looking at one of its lines (microwave ovens), where it offers three different levels of specification: Cheap which sells for £50, Average which sells for £100 and Premium which sells for £250. The production of each machine goes through four different stages and you have been provided with the following data table:

Process\Machine

Cheap

Average

Premium

Cost per hour ...