FM for Actuaries

32 CHAPTER 1
(b) It is given that
t v(t)
1 0.98
2 0.95
3 0.92
4 0.90
Find the present value of the following stream of payments:
t C t ($)
0 1,000
1 800
2 600
3 400
4 200
1.21 Let v(t) = 20
20 + t .
(a) Find i(1),i(2) and i(3).
(b) How is the interest credited?
1.22 Beda wishes to accumulate $3,000 in a fund at the end of 4 years. He makes
deposits of $K, $2K, $3K at the beginning of year 1, 2 and 3, respectively.
Find the value of K if the fund earns
(a) simple interest of 5% per year,
(b) compound interest of 5% per year.
1.23 Eddy deposits $2,000 into a savings account. The bank credits interest at
arateofi convertible yearly for the first 4 years and a nominal rate of 4i
convertible quarterly thereafter. If the accumulated value of the account is
$2,918.70 after 6 years, find the accumulated value of the account after 8.5
years.
1.24 Ada pays $1,000 today and $1,200 after 2 years to Andrew in exchange for
a payment of $2,198 one year from today.
(a) Set up an equation of value with i as unknown by equating the future
values of the two cash-flow streams.
(b) Solve the equation of value obtained in (a).
(c) What can you observe?