# Topic: Finance

3. The force of interest ‹(t) is a function of time and at any time t (measured in years) is given by: ‹(t) = ( • •t 0 t < • • • t (a) Calculate the present value of £• due at time t = •. (4 Marks) (b) Calculate the constant force of interest per annum that would produce the same present value. (2 Marks) (c) Calculate the equivalent effective annual rate of interest. (2 Marks) (d) Calculate the equivalent effective annual rate of discount. (2 Marks) (Question 3, Total: 10 Marks) 4 4. An annuity of £• per annum is payable at the end of each year for • years. Calculate the present value and the accumulated value of the annuity at the following rates: (a) an effective interest rate of •% per annum; (5 Marks) (b) an effective interest rate of •% per annum payable monthly. (5 Marks) (Question 4, Total: 10 Marks)

**For full marks, show your working **

**Numerical Answers **to appropriate number of
decimal places, with rounding to pounds and pence where appropriate

**PLAGIARISM **Ensure that all working is your own. Any
student found guilty of academic mis- conduct will be subject to the penalties
of the university should the charges be upheld.

**Learning Outcomes Assessed: **These are
• Distinguish between interest
rates expressed in different time periods and derive

the relationships between them; • Evaluate the present value and the accumulated value of a given cash flow series; • Define and derive compound interest functions including annuities certain;

**Preview Copy **You are advised to practice
these sums with relevant numbers – Say *i;i*(*p*)
= 2%*; *3%, principals of £100, 200 or
£1000 as appropriate, *p
*= 2*; *4*;
*12 and
number of years 10*;
*20. Please
note that other values will appear in the test