1. A payment of KSh.24,000 is due in 8 years time in return for KSh.4,000 now, KSh.8,000 in 5 years
and KSh.X in 10 years. If i = 8%, nd KSh.X, such that the value of both options is equal.[4 marks]
2. David can receive one of the following two payment streams:
(a) 150 at time 0, 300 at time n, and 450 at time 2n
(b) 900 at time 10
At an annual eective interest rate of i, the present values of the two streams are equal. Given
vn = 0:76, determine i. [4 marks]
3. Jane takes a home improvement loan of $11; 000 over 5 years. She makes monthly repayments in
arrears and the bank charges an eective rate of interest of 6% p.a.
(a) what is the monthly repayment. [4 marks]
(b) How much interest does she pay in the 3rd year. [4 marks]
4. Show that
(a) an =
1 ?? vn
i
[2 marks]
(b) an =
1 ?? vn
[3 marks]
(c) (Ia)n =
an ?? nvn
[5 marks]
. 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]
5. 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]
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