CA3 2005 September past paper

[Trevor]

Hi,

I am attempting past papers starting from the early years. For the 2005 September, question 1, we are asked to explain how the figures are derived.
Based on the loan statement given, I am able to derive all the figures, except the 10.6% APR.
There is a note below explaining:
"Annual Percentage Rate is the effective annual compound interest rate underlying the loan, allowing for the Acceptance Fee and the Settlement Fee."

However I am still struggling to derive the 10.6% APR.
I tried a calculation in a spreadsheet:
1. Populate the amount at each month as describe on the statement
2. Find the discount rate such that the present value of the stream of cashflow equates to the amount borrowed (13500)

The implied discount rate (or interest rate) of this calculation is 11.02%. ie: if the discount rate is 11.02%, the cashflow described has a present value of 13500.

Can anyone show me the numerical calculation on how the 10.6% is derived? I am a little bit rusty on loan calculations.

Thanks in advance!

 

[David Wilmot]

In CP3 exams there is typically the instruction: 'You must assume that any numerical information provided in this scenario material is correct unless otherwise stated.'

The APR of 10.6% should have been calculated by solving the equation that equates all the payments (including the acceptance and settlement fees) with the amount of finance. I haven't checked it - primarily as the recipient would not want this calculation to be set out in any detail - they only need to know the principles behind it, and why it differs from the interest rate being quoted and charged.

The amount owed under the loan gradually reduces to zero, so on average only half the loan is owed, i.e. £6,750. Each year £675 is being paid, so the level annual cost is about 10% of the average loan amount outstanding. The actual APR calculation is more complicated but this indicates that the 10.6% quoted is reasonable.

If anyone reproduces the exact calculation then it would be interesting to see that, but it is not needed in order to answer the communication challenge posed by this past exam question.

Best wishes

David

 

[Trevor]

Hi David,

Thank you for reminding me that for the purpose of the communication exam, a detailed calculation shouldnt be required, in fact should not be explained to a non-technical audience.
I am able to answer "his" question to confirm the repayment amounts are correct. However, I can't even explain the 10.6% myself as an advisor. Which is what this paper is testing me.

The only way I can get anywhere close to the 10.6% is:
The monthly repayment is £337.50. The annual loan capital is £3375 (=£13500/4). The monthly repayment is exactly 10% of the annual loan capital. If I say: "We split the total loan amount to four years, so we aim to pay £3375 per year, we then repay 10% of this amount each month", this will raise even more questions - paying this amount 12 times a year means it is paying 120% of it a year, which doesn't sound right at all.

on average only half the loan is owed

Can I know why is this the case? Shouldn't the whole capital amount gets paid by the end of the term?

 

[David Wilmot]

Can I know why is this the case? Shouldn't the whole capital amount gets paid by the end of the term?

The amount owed gets paid off gradually over the period of the loan. The Examiners solution (in their report) puts it neatly as: 'over the 4 years the amount you owe will reduce from £13,500 to 0, so on average will be about half that'.

 

[David Wilmot]

Hi Trevor,

One difficulty in reproducing the calculation of 10.6% is that it isn't clear whether the monthly payments are made in advance or in arrears.

If we assume that the 48 monthly payments are being made in advance then we can ignore the acceptance fee as it is paid immediately when due (and so doesn't form part of the amount borrowed). We therefore need to consider 47 payments of £337.50 and a final payment of £432.50 made one-month before the end of the 4-year period. If we assume that the settlement fee is due at the same time as that final monthly payment then it too can be ignored (as it then also doesn't form part of the amount borrowed).

With those assumptions (which craftily enable us to ignore the fees), we are looking at a loan of £13,500 repaid by 48 monthly payments of £337.50.

The present value of a series of 48 monthly payments (made at the beginning of each month) at 10.1% p.a. is £13,500.
I'm surmising that the 10.6% was derived using assumptions different to those noted above - hence the slightly different APR.

Does that help you feel more comfortable about the APR quoted Trevor?

In the exam, we clearly wouldn't be getting into any of this detail, but rather concentrate on getting across the key difference between a 'flat' interest charge, and a compound rate of interest.

David

 

[Trevor]

Hi Trevor,

One difficulty in reproducing the calculation of 10.6% is that it isn't clear whether the monthly payments are made in advance or in arrears.

If we assume that the 48 monthly payments are being made in advance then we can ignore the acceptance fee as it is paid immediately when due (and so doesn't form part of the amount borrowed). We therefore need to consider 47 payments of £337.50 and a final payment of £432.50 made one-month before the end of the 4-year period. If we assume that the settlement fee is due at the same time as that final monthly payment then it too can be ignored (as it then also doesn't form part of the amount borrowed).

With those assumptions (which craftily enable us to ignore the fees), we are looking at a loan of £13,500 repaid by 48 monthly payments of £337.50.

The present value of a series of 48 monthly payments (made at the beginning of each month) at 10.1% p.a. is £13,500.
I'm surmising that the 10.6% was derived using assumptions different to those noted above - hence the slightly different APR.

Does that help you feel more comfortable about the APR quoted Trevor?

In the exam, we clearly wouldn't be getting into any of this detail, but rather concentrate on getting across the key difference between a 'flat' interest charge, and a compound rate of interest.

David

Hi David, thank you for your explanation. It is crystal clear now. I was trying very hard to derive 10.6% exactly although this is not required in the exam, but took it as a practice to be sure I understand it. I haven't thought of the way of explaining like in the examiner report (tried to figured it out/discuss before looking at the answers).

One again, thank you