UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Actuarial Science Program
DEPARTMENT OF MATHEMATICS
Math 210
Theory of Interest
Prof. Rick Gorvett
Fall, 2015
Homework Assignment # 1 (max. points = 10)
Due at the beginning of class on Thursday, September 3, 2015
You are encouraged to work on these problems in groups of no more than 3 or 4. However, each
student must hand in her/his own answer sheet. Please show your work – enough to show that
you understand how to do the problem – and circle your final answer. Full credit can only be
given if the answer and approach are appropriate. Please give answers to two decimal places –
e.g., xx.xx% and $xx,xxx.xx .
Note: Homework assignments are due at the beginning of the class. Assignments will not be
accepted after 9:45 am on the due date.
(1)
At what annual simple interest rate will you double your money in 8 years?
(2)
At what annual compound interest rate will you double your money in 8 years?
(3)
You invest $1,000 now, at an annual simple interest rate of 10%. What is the effective
rate of interest during the 6th year of your investment?
(4)
At time 0, you invest $500 into an account earning 7.5% annual compound interest.
After n years, your account has grown to $1,500. Find n. (Determine n in years, to two
decimal places.)
(5)
At time 0, you invest $250 into an account. At time 4, you invest another $600 into the
same account. The account earns interest at an annual rate of 11%. Find the accumulated
value of your account at time 10.
(6)
Suppose that a(t) = 1+ 0.020t 2 . The only investment made is $10,000 at time 0. Find the
accumulated value of this investment at time 3.
(7)
Suppose that the accumulation function for an account is a(t) = (1+ 0.015t 2 ) . The only
investment made is $5,000 at time 2. Find the accumulated value of this investment at
time 5.
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(8)
Suppose that A(t) = α t 2 + 20 β . If $2,000 invested at time 0 accumulates to $3,000 at
time 4, find A(5) . (Hint: use the accumulated values at times 0 and 4 to determine the
values of α and β.)
(9)
On October 1, 2015, you invest $3,000 into an account earning 12% annual compound
effective interest rate. On July 1, 2018, you deposit an additional $2,000 into the
account. What is the accumulated value of your account on April 1, 2020?
(10)
On April 1, 2022, you will need $200,000. Assuming a 10% annual compound effective
rate of interest, what would you have to invest on October 1, 2015, in order for you to
fulfill that need?
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