A principal of £8,000 is invested at an annual rate of 6% interest.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. Question 1

A principal of £8,000 is invested at an annual rate of 6% interest.

(i) Determine the future value after 12 years if the interest is compounded monthly.

(ii) Determine the future value after 12 years if the interest is compounded continuously.

(iii) Derive the annual equivalent rate for each method of compounding in (i) and (ii).

(iv) If the interest is compounded continuously, how long would it take for the future value to reach

£20,000?

 

[20 Marks]

 

 

2. Question 2

An individual is looking to secure a £300,000 mortgage. The bank offers an interest rate of 4% compounded an- nually.

(i) Show that the monthly repayment (m) for borrow- ing P at interest rate r compounded annually over n years is given by:

 

r P

m =

1 — (1 + r)—n 12

 

 

(ii) Calculate the monthly repayment if they take the mortgage over 25 years.

(iii) They do not want the monthly repayment to exceed

£1,800 per month. Derive what is the minimum loan duration that satisfies this criterion.

 

Attachments:

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