The force of interest d ( )t is a function of time and at any time t , measured in years, is given by the formula:
d Ï + £< = Ì
Ó £
0.04 0.02 0 5 ( ) 0.05 5
t t
t
t
(i) Derive and simplify as far as possible expressions for v t( ) , where v t( )
is the present value of a unit sum of money due at time t . [5]
(ii) (a) Calculate the present value of £1,000 due at the end of 17 years.
(b) Calculate the rate of interest per annum convertible monthly implied
by the transaction in part (ii)(a). [4]
A continuous payment stream is received at a rate of 0.01 10 t e units per
annum between t = 6 and t = 10 .
(iii) Calculate the present value of the payment stream.