Hi.. plz need a complete solution to this ques.. can anybody help... plz plz plz... actuarial science related?

ct1 actuarial science


Question 1


a) As of September 2009, for loans of between £10,000 and £25,000, the Royal Bank of


Scotland (RBS) typically charges an effective annual rate of interest (also known as the


“Annual Percentage Rate” or APR) of 11.4%.


Calculate the level monthly repayment for a loan of £10,000 which is to be repaid over 5


years.


[3]


b) For a loan of £5,000, repayable monthly in arrears over 5 years, the level monthly


repayment required is £111.68. And, for a loan of £1,000, repayable monthly in arrears over


5 years, the level monthly repayment required is £26.26.


Calculate the APR (rounded to the nearest 0.1%) for each of these smaller loan amounts.


Note: You may want to use the “Solver” function in Excel to help here.


[4]


c) Give two possible reasons why the APR decreases as the amount of the loan increases and


briefly explain1 your answer in each case.


[4]


d) Alternatively, give one reason why you might expect the APR to increase as the amount of


the loan increases.


[2]


e) The RBS website states that these quotes are “for illustration purposes only” and that “the


actual rate you will be charged will depend on an assessment of your individual


circumstances”.


Give five distinct examples of “individual circumstances” that may result in the APR charged


for a loan being higher than the “typical” rates quoted above and explain briefly why in each


case.


[10]


f) Alternatively, homeowners may be able to borrow similar amounts at a significantly lower


APR. Explain briefly why this is the case.


[2]


[Total 25]


1 According to the dictionary, “explain” means “to make clear the cause or reason of” ... please bear this in


mind when giving your answer to this and other questions!


Question 2


You are interested in buying a house costing £200,000 and have a maximum deposit of £50,000.


Thus, you need to find a mortgage for £150,000, which you intend to repay over a 25-year period,


and you have narrowed the choice down to the following possibilities:


1) A five-year fixed-rate repayment mortgage from Lloyds TSB.


As of October 2009, this is based on a fixed-rate of interest of 5.89% per annum


convertible monthly for the first five years. At the end of this period, the rate of interest


(again, convertible monthly) changes to the bank’s Standard Variable Rate (which is


defined to be 2% above the then current Bank of England base rate – which, as of


October 2009, is equal to 0.5% per annum).


In addition, there is a product fee of £995, which is added to the initial mortgage


amount (although, in practice, can be paid in full at the outset).


2) A life-time tracker repayment mortgage from HSBC.


As of October 2009, this is based on a variable rate of interest (convertible monthly)


equal to the current Bank of England base rate – of 0.5% per annum – plus 2.99%.


In addition, there is a booking fee of £599, which must be paid as a lump sum at the


outset.


a) For each of the two mortgages above, calculate:


(i) the initial monthly repayment amount,


In addition, for the five-year fixed-rate mortgage, calculate the expected monthly


repayment amount after the end of the five-year fixed-rate period.


(ii) the total cost of the loan (i.e. the total amount repaid including the fees),


(iii) the APR on each loan (expressed as the effective rate of interest per annum, quoted


to the nearest 0.1%).


[18]


b) Despite the fact that the five-year fixed-rate mortgage is considerably more expensive,


explain the key advantage in choosing this mortgage over the life-time tracker mortgage.


Also, comment on why such an advantage might be particularly attractive in the current


economic climate.


[4]


c) Whilst there are a few mortgage packages available in the market with a fixed-rate period of


longer than five years (indeed, the maximum currently available is 15 years), such


arrangements are unusual.


Give two possible reasons why longer term fixed-rate mortgages are so uncommon.


[4]


d) If the loan-to-value ratio (LVR), defined as the ratio of the initial mortgage amount to the


value of the property, is greater than 75%, then the rate of interest charged by Lloyds TSB


during the five-year fixed-rate period is increased from 5.89% per annum to 6.99% per


annum (with the rate of interest after this period remains unchanged).


Explain why this is the case.


[2]


e) Alternatively, for the life-time tracker mortgage, the initial booking fee of £599 can be


avoided by choosing a nil-fee version with a rate of interest convertible monthly equal to the


Bank of England base rate plus 3.29% for the entire term of the loan.


Discuss the advantages and disadvantages of the choosing this option over the standard lifetime


tracker mortgage.


[4]


f) A friend of yours, who has little financial knowledge, has suggested that you could save a lot


of money by taking out an interest-only mortgage.


He recommends a life-time tracker mortgage from ING Direct, where the rate of interest


convertible mont|||So you can't use computers? These are all elementary calculations. I still have my old HP 12C from about 30 years ago, but sadly the batteries are run down. Surely there is a financial calculator and accompanying instruction docs that cover just this sort of problem.