1. 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.
(b) Find the present value (at time t = 0) of an investment of 15 due at time t = 20.
(c) Find the constant force of interest which would lead to the same present value in (ii) being
obtained.
(d) What is the eective rate of interest from time t = 8 to time t = 9. [14 marks]
2. An annuity is paid half-yearly in arrears at a rate of KSh.18,000 per annum, for 20 years. The rate
of interest is 6% per annum eective in the rst 13 years and 7% per annum convertible quarterly for
the remaining 7 years. Calculate the accumulation of the annuity at the end of 20 years. [4 marks]
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