1) The force of interest (t) at time t is at+bt2 where a and b are constants. An amount of 1000 invested
at time t = 0 accumulates to 1500 at time t = 5 and 2300 at time t = 10. Determine the value of a
and b. [5 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<
:
0:06 0 t 5
0:01(t2 ?? t) 5 < t
3)(a) Calculate the present value of a unit sum of money due at time t = 10. [4 marks]
(b) Calculate the eective rate of interest over the period t = 9 to t = 10. [3 marks]
(c) In terms of t, determine an expression for v(t), the present value of a unit sum of money due
during the period 0 < t 5. [1 mark]
(d) Calculate the present value of a payment stream paid continuously for the period 0 < t 5,
where the rate of payment, (t), at time t, is e0:04t. [4 marks]
4) You are given that the nominal rate of discount per annum convertible every 2 months is 15%. Calculate
the product of the equivalent nominal rate of interest per annum convertible every three months i(4)
and the force of interest . [6 marks]
5) A fund is earning 7% simple interest. Find the year when this will be equivalent to an eective rate
of 4:7%. [3 marks]
6) June borrows KSh.50,000 for 10 years at an annual eective interest rate of 10%. She can repay this
loan using the amortization method with payments of KSh.8,137.25 at the end of each year. Instead,
June repays the KSh.50,000 using a sinking fund that pays an annual eective interest rate of 14%.
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