Actuarial Mathematics
Pre-Test Questions
Course Introduction
Actuarial Mathematics is a course that introduces students to the fundamental mathematical concepts and techniques used in the actuarial profession. The course covers topics such as probability theory, life tables, survival models, life insurance and annuity calculations, premium determination, and risk assessment. Students will learn how to analyze and model financial and insurance risks, evaluate contingent cash flows, and apply mathematical tools to real-world problems involving uncertainty in the fields of insurance, finance, and pension planning. This course emphasizes the application of rigorous mathematical reasoning to solve problems relevant to actuarial science and prepares students for professional actuarial exams.
Recommended Textbook
Mathematics of Finance 8th Edition by Robert Brown
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8 Chapters
674 Verified Questions
674 Flashcards
Source URL: https://quizplus.com/study-set/3487 Page 2
Chapter 1: Simple Interest and Simple Discount
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118 Verified Questions
118 Flashcards
Source URL: https://quizplus.com/quiz/69258
Sample Questions
Q1) Interest of $300 is charged on a loan of $7300 bearing interest at r = 11%.What was the term of the loan? (Answer to the nearest day)
A)131 days
B)134 days
C)136 days
D)142 days
Answer: C
Q2) You have two options available in repaying a loan.You can pay $200 at the end of 5 months and $300 at the end of 10 months or you can pay $X at the end of 3 months and $2X at the end of 6 months.What is X if the simple interest rate is 6% and the focal date is at the end of 5 months.
A)$169.16
B)$168.05
C)$164.22
D)$163.14
Answer: C
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3
Chapter 2: Compound Interest
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127 Verified Questions
127 Flashcards
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Sample Questions
Q1) A person invests in a fund earning interest at j<sub>2</sub> = 6%.The annual rate of inflation is 2% in year 1,2.5% in year 2,and 3.0% in year 3.What is the annual real interest rate,compounded once a year,earned over the 3-year period?
A)3.42%
B)3.47%
C)3.50%
D)3.59%
Answer: C
Q2) You owe your parents $2500 today.You agree to pay this back by making a payment of $500 now,$600 six months from now and $X 18-months from now.What is X if j<sub>4</sub> = 6%?
A)$1417.60
B)$1473.22
C)$1482.36
D)$1550.07
Answer: D
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Chapter 3: Simple Annuities
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67 Verified Questions
67 Flashcards
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Sample Questions
Q1) You deposit $100 every three months for the next 50 years,first deposit made today.If the interest rate is j<sub>4</sub> = 10%,how much do you have three months after your last deposit?
A)$582,417
B)$568,212
C)$568,112
D)$554,256
Answer: C
Q2) Jim just turned age 65.He takes his RRSP savings of $300,000 and buys a 20-year annuity that pays him $R every month.If the interest rate is j<sub>12</sub> = 7.2% and the first payment is at age 65,what is R?
A)$2376.22
B)$2366.48
C)$2362.05
D)$2347.96
Answer: D
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Chapter 4: General and Other Annuities
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79 Flashcards
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Sample Questions
Q1) You deposit $5000 every year into a fund earning interest at j<sub>2</sub> = 7%,starting on your 30<sup>th</sup> birthday with your final deposit made on your 65<sup>th</sup> birthday.How much have you accumulated on your 65<sup>th</sup> birthday? (Answer to nearest dollar)
A)$691,184
B)$709,921
C)$744,567
D)$765,485
Q2) You deposit $A today in a fund paying interest at j<sub>4</sub> = 8%.You plan to make quarterly withdrawals for 5 years,starting 3 months from now.The first withdrawal is $500,with each succeeding withdrawal increasing by 3%.What is A?
A)$8,950.24
B)$9,129.25
C)$10,773.05
D)$10,988.52
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6
Chapter 5: Repayment of Debts
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85 Verified Questions
85 Flashcards
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Sample Questions
Q1) A city borrows $1 million,paying semi-annual interest at j<sub>2</sub> = 6%.The city creates a sinking fund in which semi-annual deposits of $35,360.93 are made in order to accumulate the $1 million needed to repay the loan upon maturity.The sinking fund ends earns j<sub>2</sub> = 7%.You are given that the book value of the debt immediately after the 12<sup>th</sup> payment is $483,661.06.How much has been accumulated in the sinking fund immediately after the 13<sup>th</sup> deposit of $35,360.93?
A)$516,338.94
B)$534,410.81
C)$535,950.12
D)$569,771.73
Q2) Exactly five years ago,a $100,000 condominium was purchased by making a $65,000 down payment and taking out a $35,000 mortgage.The mortgage interest rate was j<sub>2</sub> = 8% and monthly mortgage payments of $267.10 have been made at the end of each month for the past five years.What is the purchaser's equity (buyer's equity)position today? (Answer to nearest dollar)
A)$32,249
B)$67,249
C)$67,751
D)$80,441
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7
Chapter 6: Bonds
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Sample Questions
Q1) A $1000 bond with semi-annual coupons is redeemable for $1030 in 5 years.The write-down (book value adjustment)in the 1<sup>st</sup> coupon period is $4.09.What is the price of the bond to yield j<sub>2</sub> = 9%?
A)$949.74
B)$979.74
C)$1050.26
D)$1080.26
Q2) For a $10,000 bond with semi-annual coupons,you are given the following: The redemption value is $10,400
The book value one period before the redemption date is $10,347.57 Interest on the book value in the last coupon period is $369.93 What is the bond coupon rate,j<sub>2</sub>?
A)6.35%
B)7.15%
C)7.40%
D)8.45%
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Chapter 7: Business Decisions, Capital Budgeting and Depreciation
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66 Flashcards
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Sample Questions
Q1) A delivery van costing $24,000 has an estimated lifetime of 12 years at which time it will cost $1200 to dispose of it.Annual maintenance costs are $900.If the interest rate is j<sub>1</sub> = 9%,what is the capitalized cost of the van? (Answer to the nearest dollar)
A)$45,378
B)$46,578
C)$47,902
D)$49,102
Q2) You are given: F<sub>0</sub> = initial investment,F<sub>1</sub>,F<sub>2</sub>, ,F<sub>n</sub> are the future net cash flows (where each is > 0).You are told that the sum of the future cash flows exceeds the initial investment.That is,
(F<sub>1</sub> + F<sub>2</sub> + + F<sub>n</sub>)> F<sub>0</sub>.Which of the following statements is (are)true?
(I)IRR must be greater than 0.
(II)NPV must be greater than 0.
A)I only
B)II only
C)I & II are true
D)Neither are true
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Chapter 8: Contingent Payments
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42 Verified Questions
42 Flashcards
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Sample Questions
Q1) For an investment of $20,000 today at j<sub>2</sub> = 4%,you expect to receive three payments of $R,one each at the end of 1,2 and 3 years.The probability of default of the first payment is 3%,while the probability of default of the 2<sup>nd</sup> or 3<sup>rd</sup> payment,given that the previous payments were made,is 3%.What should the value of R be?
A)$6996.07
B)$7212.44
C)$7429.87
D)$7435.51
Q2) A 10-year $5000 par value bond pays interest at j<sub>2</sub> = 7%.The probability that a payment is defaulted,given that all previous payments were made,is 3%.What is the purchase price to yield j<sub>2</sub> = 6%.
A)$3264.29
B)$3482.77
C)$5210.78
D)$5293.83
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