FM for Actuaries

20 CHAPTER 1
The answers to (b) and (c) are, respectively,
1
(1 + 0.06) 5 = 0.7473
and
1
(1 + 0.06) 6.5 = 0.6847.
Example 1.16: An insurance agent offers a policy that pays a lump sum of
$50,000 five years later. If the effective rate of interest is 8%, how much would you
pay for the plan?
Solution: The fair amount to pay for this policy is the present value of the lump
sum, which is equal to
50,000
(1.08) 5 = $34,029.16.
Example 1.17: A person wants to accumulate $100,000 eight years from today
to sponsor his son’s education. If an investment plan offers him 8% compounded
monthly, what amount must he invest today?
Solution: We first calculate the effective rate of interest, which is
[
1+ 0.08 ] 12
− 1=8.30%.
12
The amount required today is
100,000
(1.083) 8 = $52,841.16.
We now denote
v = 1
1+i , (1.30)
which is the present value of 1 due 1 year later. It is also called the discount
factor, as multiplying a payment at the end of the year by v gives its present value.
Combining (1.17) and (1.30), we obtain
d = iv, (1.31)