Act 2120
University Of Manitoba Actuarial Club – 2016/2017
Interest Theory Midterm 2 – Time: 70 min
1) The following table shows the annual effective interest rates being credited by an investment
account, by calendar year of investment. The investment year method is applicable for the first 3 years,
after which a portfolio rate is used:
Calendar Year
of Investment
1990
1991
1992
1993
1994
Investment Yr. Rates
i1
i2
i3
10%
10%
t%
12%
5%
10%
8%
(t - 2)%
12%
9%
11%
6%
7%
7%
10%
Calendar Year of
Portfolio Rate
1993
1994
1995
1996
1997
Portfolio Rate
8%
(t - 1)%
6%
9%
10%
Sophie makes an investment of 100 at the beginning of years 1990, 1991, and 1992. The total amount of
interest credited by her fund during the year 1993 is equal to $28.40. Calculate t.
2) You are given the following information about the activity in two different investment accounts:
Date
January 1, 2015
July 1, 2015
October 1, 2015
December 31, 2015
Account K
Fund Value Before
Activity
100.0
125.0
110.0
125.0
Date
January 1, 2015
July 1, 2015
December 31, 2015
Account L
Fund Value Before
Activity
100.0
125.0
105.8
Activity
Deposit
Withdrawal
X
2X
Activity
Deposit
Withdrawal
X
During 2015, the dollar-weighted return for investment account K equals the time-weighted return for
investment account L, which equals i. Calculate i.
3) Patrick borrows $10,000 for 10 years at an annual effective interest rate of i. He accumulates the
amount necessary to repay the loan by using a sinking fund. He makes 10 payments of X at the end of
each year, which includes interest on the loan and the payment into the sinking fund, which earns an
annual effective rate of 8%. If the annual effective rate of the loan had been 2i, his total annual payment
would have been 1.5X. Calculate i.
Act 2120
University Of Manitoba Actuarial Club – 2016/2017
4) A continuously increasing annuity with a term of n years has payments payable at an annual rate t at
time t. The force of interest is equal to 1/n. Calculate the pre sent value of this annuity in terms of n.
5) A fund is built with annual payments increasing by $1 from $1 to $10 and then decreasing by $1 to $0.
The first payment of $1 is made today. If the fund is used to purchase a 10 year level annuity with the
first payment at 20 years from today, what is the amount of the level payment? Assume an annual
effective rate of interest of 4%.
6) Calvin wishes to purchase a top-market stereo system so he and his neighbours could both listen to
his favorite album, Beyoncé’s ”Lemonade.” He is offered the following payment options:
Option 1:
Option 2:
$0 down
$432 in 1 year
$300 in 2 years
$86.56 down
$250 in 1 year
$400 in 2 years
Determine the range of interest rates for which the present value of Option 1 is less than the present
value of Option 2.
7) A loan, at a nominal annual interest rate of 24% convertible monthly, is to be repaid with equal
payments at the end of each month for 2n months. The nth payment consists of equal payments of
interest and principal. Calculate n.
8) You are given a perpetual annuity-immediate with annual payments increasing in geometric
progression, with a common ratio of 1.07. The annual effective interest rate is 12%. The first payment is
$1. Calculate the PV of this annuity.
9) Martin borrows $10,000 for 25 years, at an effective annual interest rate of 5%. A sinking fund is used
to accumulate the principal by means of 25 annual deposits earning an effective annual interest rate of
4%. Calculate the sum of the net amount of interest paid in the 13th installment and the increment in the
sinking fund for the ninth year.
Disclaimer: this exam is not one that has actually been previously tested in Interest Theory. This was
an exam created by UMAC in order to provide students with a more recent realistic representation of
what one may expect on both Interest Theory Exams, and Exam FM. There is a strong possibility that
this exam is of easier difficulty than what will be tested in Interest Theory.
- Sergiu Buda