FM for Actuaries

Interest Accumulation and Time Value of Money 35
1.37 Calculate the future value of an investment at t =5consisting of a payment
of 1 at t =2and a payment of 3 at t =4,if
(a) a(t) =1+0.05t,
(b) a(t) =(1.05) t ,
(c) δ(t) =0.05t.
1.38 In Fund P, money accumulates at a force of interest δ(t) whose graph is given
below.
(t)
0.05
1
t
(a) Find a(5).
(b) Fund Q accumulates at a constant force of interest δ Q .Ifthevalueof
the two funds are equal at t =0and t =5,findδ Q .
1.39 You are given the following stream of cash flows:
t 0.5 1 1.5 2 2.5 3
C t 10 10 10 10 10 110
Find the present value of the cash flows given that the nominal rate of interest
is 8% compounded half-yearly.
1.40 Certificates of deposit (CDs) are short- to medium-term investment instruments
issued by banks which provides a fixed rate of interest for a period of
time. CDs offer stability in interest earned but have penalty for early withdrawal.
A 1-year CD pays a nominal rate of interest of 8% compounded quarterly.
You are offered two options of penalty for early withdrawal: