1. Assuming an interest rate of 12% pa convertible monthly,
(a) Calculate the combined present value of an immediate annuity payable monthly in arrears such
that payments are KSh.100,000 pa for the rst 6 years and KSh.40,000 pa for the next 4 years,
together with a lump sum of KSh.200,000 at the end of the 10 years. [3 marks]
(b) Calculate the amount of the level annuity payable continuously for 10 years having the same
present value as the payments in (i). [3 marks]
(c) Calculate the accumulated values of the rst 7 years” payments at the end of the 7th year for the
payments in (i) and (ii). [4 marks]
2. The force of interest (t) is a function of time and at any time t (measured in years) is given by the
formula
(t) =
8>>><
>>>:
0:03 + 0:001t2 0 t < 7
0:01t 7 t < 10
0:1 10 t
(a) An investment of 1 is made at time t = 4. Find the value to which it will have accumulated by
time t = 6:5. [5 marks]
(b) Find the present value (at time t = 0) of an investment of 15 due at time t = 20. [4 marks]
(c) Find the constant force of interest which would lead to the same present value in (ii) being
obtained. [3 marks]
(d) What is the eective rate of interest from time t = 8 to time t = 9. [2 marks]
3
STA 2191 Jane Akinyi Aduda
4. You are given that the nominal rate of discount per annum convertible every 2 months is 15%. Calculate
the nominal rate of interest per annum convertible every three months. [3 marks]
5. A fund is earning 7% simple interest. Calculate the eective interest rate in the 8th year. [2 marks]
6. At a certain simple rate of interest, 1,000 will accumulate to 1,110 after a certain period of time. Find
the accumulated value of 500 at a simple rate of interest three fourths as great over twice as long a
period of time. [2 marks]
7. Dene the accumulation factor A(t; t + h) and give the formula for the force of interest (t) per unit
time in terms of the accumulation factor. [3 marks]
28. Given a nominal interest rate of 7:5% convertible semi-annually, determine the sum of the force of
interest, ; and nominal discount rate compounded monthly, d(12). [5 marks]
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