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This page indicates changes made to Study Note FM-09-05.
April 28, 2014: Question and solutions 61 were added.
January 14, 2014: Questions and solutions 58–60 were added.
Copyright 2013 by the Society of Actuaries.
Some of the questions in this study note are taken from past SOA/CAS examinations.
These questions are representative of the types of questions that might be asked of candidates sitting for the new examination on Financial Mathematics (2/FM). These questions are intended to represent the depth of understanding required of candidates. The distribution of questions by topic is not intended to represent the distribution of questions on future exams.
Kathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i.
The accumulated amount in the account at the end of 40 years is X , which is 5 times the accumulated amount in the account at the end of 20 years.
Calculate X.
Eric deposits 100 into a savings account at time 0, which pays interest at a nominal rate of i , compounded semiannually.
Mike deposits 200 into a different savings account at time 0, which pays simple interest at an annual rate of i.
Eric and Mike earn the same amount of interest during the last 6 months of the 8th^ year.
Calculate i.
An association had a fund balance of 75 on January 1 and 60 on December 31. At the end of every month during the year, the association deposited 10 from membership fees. There were withdrawals of 5 on February 28, 25 on June 30, 80 on October 15, and 35 on October 31.
Calculate the dollar-weighted (money-weighted) rate of return for the year.
A perpetuity costs 77.1 and makes annual payments at the end of the year. The perpetuity pays 1 at the end of year 2, 2 at the end of year 3, …., n at the end of year ( n +1). After year ( n +1), the payments remain constant at n. The annual effective interest rate is 10.5%.
Calculate n.
You are given the following table of interest rates:
Calendar Year of Original Investment Investment Year Rates (in %)
Portfolio Rates (in %) y i 1 y^ i 2 y^ i 3 y^ i 4 y^ i 5 y^ iy + 1992 8.25 8.25 8.4 8.5 8.5 8. 1993 8.5 8.7 8.75 8.9 9.0 8. 1994 9.0 9.0 9 .1 9.1 9.2 8. 1995 9.0 9.1 9.2 9.3 9.4 9. 1996 9.25 9.35 9.5 9.55 9.6 9. 1997 9.5 9.5 9.6 9.7 9. 1998 10.0 10.0 9.9 9. 1999 10.0 9.8 9. 2000 9.5 9. 2001 9.
A person deposits 1000 on January 1, 1997. Let the following be the accumulated value of the
1000 on January 1, 2000:
P : under the investment year method
Q : under the portfolio yield method
R : where the balance is withdrawn at the end of every year and is reinvested at the new
money rate
Determine the ranking of P , Q , and R.
(A) P Q R (B) P R Q
(C) Q P R
(D) R P Q (E) R Q P
A 10,000 par value 10-year bond with 8% annual coupons is bought at a premium to yield an annual effective rate of 6%.
Calculate the interest portion of the 7th^ coupon.
A perpetuity-immediate pays 100 per year. Immediately after the fifth payment, the perpetuity is exchanged for a 25-year annuity-immediate that will pay X at the end of the first year. Each subsequent annual payment will be 8% greater than the preceding payment.
The annual effective rate of interest is 8%.
Calculate X.
Ernie makes deposits of 100 at time 0, and X at time 3. The fund grows at a force of interest
2 t 100
The amount of interest earned from time 3 to time 6 is also X.
Calculate X.
Mike buys a perpetuity-immediate with varying annual payments. During the first 5 years, the payment is constant and equal to 10. Beginning in year 6, the payments start to increase. For year 6 and all future years, the current year’s payment is K % larger than the previous year’s payment.
At an annual effective interest rate of 9.2%, the perpetuity has a present value of 167.50.
Calculate K, given K < 9.2.
A loan is amortized over five years with monthly payments at a nominal interest rate of 9%
compounded monthly. The first payment is 1000 and is to be paid one month from the date of the loan. Each succeeding monthly payment will be 2% lower than the prior payment.
Calculate the outstanding loan balance immediately after the 40th^ payment is made.
To accumulate 8000 at the end of 3 n years, deposits of 98 are made at the end of each of the first
n years and 196 at the end of each of the next 2 n years.
The annual effective rate of interest is i. You are given (l + i ) n^ = 2.0.
Determine i.
