Download ACT 240H1F F06 Term Test 1 Privacy ID A v07

Your name:__________________________
Your student ID:______________________
UNIVERSITY OF TORONTO
ACT240H1F
TERM TEST 1 10:00 am Oct 13, 2006
Instructor: Keith Sharp PhD FSA
NOTES:
1. Calculators allowed
2. It’s OK to write on book. If you also use scrap, please submit it with this book.
3. This is a closed book exam.
4. Multiple choice: only your blobs on the Scantron sheetwill be graded.
5. 10 points correct, two if blank, zero points if wrong
6. So expectation if you guess is the same as leaving a blank.
7. Timing: 50 minutes
8. Make sure you’ve indicated your letter answers on the Scantron sheet before time’s up
9. Please stay in your seats and don’t talk till all question papers have been collected.
10. Photo ID on desk during exam please.
11. Name and student ID at top of this question paper please.
12. For purposes of identifying your privacy ID, please code question 11 with the privacy ID
(A), (B), (C) or (D) indicated in the footer of this and every page.
13. Good luck!
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UNIVERSITY OF TORONTO: ACT240H1F FALL 2006 TEST 1
1.
(01-004 Brov3-Ex. 1.1.18(b)-Mdfd) At an effective annual compound interest rate of
i>0, it is found that an investment doubles in a years, triples in b years, and 1 grows to 5 in c
years
To what exact amount does 10 grow in 3a+3b years?.
(A) $1,960
(B) $2,060
(C) $2,160
(D) $2,170
(E) The correct answer is not given by (A), (B), (C) or (D)
2.
(01-013 Brov3-Ex. 1.1.2a-Mdfd) Unit values in a mutual fund have experienced annual
growth rates of 10%, 26%, -7%, 4% and 17% in the past five years. The fund manager suggests
that the fund can advertise an average growth rate of 10% over the past five years. What is the
actual compound growth rate over the past five years?
(A) Less than 9.500%
(B) 9.500% but less than 10.000%
(C) 10.000% but less than 10.500%
(D) 10.500% but less than 11.000%
(E) 11.000% or more
3.
(01-010 F06TT1 FMmanF06-PS01-Q01-SOA-Modfd) Gertrude deposits 10,000 in a
bank. During the first year, the bank credits an annual effective interest rate of i. During the
second year, the bank credits an annual effective rate of interest i-5%. At the end of two years,
she has 12,093.75 in the bank. What would Gertrude have in the bank at the end of four years, if
the annual effective rate of interest were i+9% for each of the four years? Give the answer to the
nearest $10
(A) 15,720
(B) 15,820
(C) 15,920
(D) 16,020
(E) The correct answer is not given by (A), (B), (C) or (D)
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UNIVERSITY OF TORONTO: ACT240H1F FALL 2006 TEST 1
4.
(01-038 F06TT1 FMmanF06-PS03-Q08-SOA-Modfd) An investment fund is
established at time 0 with a deposit of 5000. 1000 is added at the end of 4 months, and an
additional 4000 is added at the end of 8 months. No withdrawals are made. The fund value,
including interest, is 10560 at the end of 1 year. The force of interest at time t is k/[1+(1-t)k]
for 0≤t≤1. Determine k.
(A) 0.030 but less than 0.050
(B) 0.050 but less than 0.070
(C) 0.070 but less than 0.090
(D) 0.090 but less than 0.110
(E) 0.110 or more
5.
(02-079 F06TT1 FMmanF06-PS06-Q02) Smith borrows 100,000 on Jan. 1, 1999. She
repays the loan with 20 annual payments starting Jan. 1, 2000. The payments in even years
(2000, 2002, ...) are each of amount 2X, and the payments in odd years are each of amount 2Y.
You are given that the annual effective rate of interest is 0.05, and the total of all 20 loan
payments is 160,000. Find X .
(A) Less than 5000.00
(B) 5000.00 but less than 6000.00
(C) 6000.00 but less than 7000.00
(D) 7000.00 but less than 8000.00
(E) 8000.00 or more
6.
(01-010 F06TT1 Brov3-Ex. 1.3.4 Modified v02) Eric deposits X into a savings account at
time 0, which pays interest at a nominal rate of i, compounded semiannually.
Mike deposits 1.4X 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.
(A)
(B)
(C)
(D)
(E)
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Less than 5.000%
5.000% but less than 6.500%
6.500% but less than 8.000%
8.000% but less than 9.000%
9.000% or more
UNIVERSITY OF TORONTO: ACT240H1F FALL 2006 TEST 1
7.
This ad could appear in Varsity:
Only 3% interest per annum (compounded monthly)! Pay for your $10,000 thneed in 48 easy
monthly payments, starting one month from now! Or get a $X discount if you pay in a cash
lump sum!
The merchant is using the current market interest rate of 6% per annum compounded monthly
for her calculations, and wants the same profit on a cash sale as on an ‘easy payments’ sale.
Calculate X. (Note that $560.000 means exactly $560)
(A)
Less than $560.000
(B)
$560.000 but less than $570.000
(C)
$570.000 but less than $580.000
(D)
$580.000 but less than $590.000
(E)
$590.000 or more
8.
Your grandparents as a ‘gift’ set you up with a 60 month Bell Mobility contract at
$120 per month payable at the end of each month. Just after the 5th. payment, a competitor
offers a no-commitment (no lock-in contract) deal at $70 per month. You make the assumption
that the $70 rate will continue for a long time. Calculate the maximum penalty X you are
willing to pay Bell Mobility to escape their deal. Use an interest rate of 1% per month. Give
the answer to the nearest dollar.
(A)
(B)
(C)
(D)
(E)
Less than $2,100.000
$2,100.000 but less than $2,200.000
$2,200.000 but less than $2,300.000
$2,300.000 but less than $2,400.000
More than $2,400.000
9.
Your bank savings account is currently empty. The bank pays interest of 6% per year,
compounded monthly. Your friend Chiu tends to spend every dollar quickly, and would like a
weekly income as security. Chiu is happy to pay you an initial $X lump sum to put into your
savings account to fund this setup. Chiu needs 52 payments of $250 per week, first payment a
week from now. Calculate X. Assume 52 weeks in a year and 12 months in a year.
(A)
(B)
(C)
(D)
(E)
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Less than $12,500.00
$12,500.00 but less than $12,600.00
$12,600.00 but less than $12,700.00
$12,700.00 but less than $12,800.00
More than $12,800.00
UNIVERSITY OF TORONTO: ACT240H1F FALL 2006 TEST 1
10.
Telus, marketing to U of T students, offers you a ‘free’ phone if you sign up for a 12
month contract at $100 per month, payable at the end of each month. Rogers offers no phone
but the same quality of phone service at $70 per month if you commit to a 12-month contract.
Your bank pays 4% per annum effective and you decide to use that rate for your comparison.
Calculate the minimum phone value which would make you choose Telus.
(A)
(B)
(C)
(D)
(E)
Less than $351.000
$351.000 but less than $352.000
$352.000 but less than $353.000
$353.000 but less than $354.000
More than $354.000
11.
For purposes of identifying your privacy ID, please code question 11 with the privacy ID
(A), (B), (C) or (D) indicated in the footer of this and every page.
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