Your name:__________________________
Your student ID:______________________
UNIVERSITY OF TORONTO
ACT240H1F
TERM TEST 2 6:00 pm June 7, 2007
Instructor: Keith Sharp PhD FSA CFA
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: 60 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 13 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 SUMMER 2007 TEST 2
1. (Lecture May 24, 2007) A bathroom remodeling firm quotes its price as $15,000 and
promises that it will lend you all the money at a bargain rate of only 6% per annum
compounded monthly. The loan is repaid with level payments at the end of each month for five
years. Alternatively, you can get a discount of $X if you pay fully in cash now. The firm, using
the actual market interest rate of 9% per annum compounded monthly, calculates X to give the
same profit whichever option you choose. Calculate $X.
(A)
Less than $1,020.00
(B)
$1,020.00 but less than $1,040.00
(C)
$1,040.00 but less than $1,060.00
(D)
$1,060.00 but less than $1,080.00
(E)
$1,080.00 or more
2. (May 29 Assignment) On January 1, 2000 Smith borrows an amount L with the following 10year payment scheme. 2000 at the end of each even-numbered year, 4000 at the end of each
odd-numbered year. The final payment will be made in 2009. Find L (nearest 1,000) assuming
annual effective interest 8%.
(A)17,000
(B) 18,000
(C) 19,000
(D) 20,000
(E) The correct answer is not given by (A), (B), (C) or (D)
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2007 TEST 2
3. (Assignment May 29, 2007) Victor wants to purchase a perpetuity paying 300 per year with
the first payment due at the end of year 11. He can purchase it by either:
(i) paying P per year at the end of each year for 10 years, where P=240; or
(ii) paying K per year at the end of each year for the first 5 years and nothing for the next 5
years.
Calculate K to the nearest 10
(A) 400
(B) 420
(C) 440
(D) 460
(E) The correct answer is not given by (A), (B), (C) or (D)
4. (Assignment May 31, 2007) Smith borrows $820 on July 1, 1984 . He repays the loan with
semi-annual payments (every Dec. 31 and June 30) beginning Dec. 31, 1984 . The Dec. 31
payments are each $30 and the June 30 payments are each $60. Payments continue in this way
for as long as necessary until the loan is completely repaid. A smaller final payment will be
necessary one-half year after the final regularly scheduled payment. If i(2) = .08 , the amount of
the smaller final payment lies in which of the following intervals?
(A) <46.000
(B) [46.000,48.000]
(C) (48.000,50.000]
(D) (50.000,52.000]
(E) >52.000
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2007 TEST 2
5. (Assignment June 5, 2007) Amy invests 3000 at an effective annual rate of 14% for 10 years.
Interest is payable annually and is reinvested at an annual rate of i. At the end of 10 years the
accumulated interest is 7023.24. Bob invests 450 at the end of each year for 20 years at an
annual effective rate of 15%. Interest is payable annually and is reinvested at an annual effective
rate of i. Find Bob's accumulated interest at the end of 20 years.
(A) Less than 27,100.00
(B) 27,100.00 but less than 27,200.00
(C) 27,200.00 but less than 27,300.00
(D) 27,300.00 but less than 27,400.00
(E) 27,400.00 or more
6. You deposit $100,000 into an account at Blue Bank at time 0. At times 1, 2, 3,…..10 Blue
Bank pays 5% interest (per annum effective rate) and you pay the interest into Red Bank,
which pays interest annually at 7% per annum effective. Every year you pay the Red Bank
interest into Green Bank, and you let it accumulate there at 9% per annum interest effective.
Just after time 10 you withdraw all your money from all three banks. Calculate the total of your
withdrawals
(A)
Less than $165,400.00
(B)
$165,400.00 but less than $165,500.00
(C)
$165,500.00 but less than $165,600.00
(D)
$165,600.00 but less than $165,700.00
(E)
$165,700.00 or more
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2007 TEST 2
7. You take out a loan for $50,000 and pay interest only on the loan, at a rate of 5% per annum
effective, at the end of each year, until repaying the principal at the end of 10 years. You
accumulate the principal by making level payments at the start of each year for 10 years in an
account which pays 4% per annum. Calculate the amount by which your total payments, totaled
over the 10 years, are less than they would be under the more usual ‘payments at end of year’
sinking fund arrangement.
(A)
Less than $410.00
(B)
$410.00 but less than $415.00
(C)
$415.00 but less than $420.00
(D)
$420.00 but less than $425.00
(E)
$425.00 or more
8. You borrow $50,000 at a rate of interest of 8% per annum effective at January 1, 2009 and
repay it by level payments on January 1, 2010, January 1, 2011…….January 1, 2019. Calculate
(using a rate of zero for discounting) the total interest that you pay.
(A)
Less than $21,000.00
(B)
$21,000.00 but less than $22,000.00
(C)
$22,000.00 but less than $23,000.00
(D)
$23,000 but less than $24,000.00
(E)
$24,000.00 or more
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2007 TEST 2
9. (Lecture May 29, 2007) Analysts expect UTSG stock to pay a dividend of $5.00 twelve
months from now, whether the economy is good or bad, but that all dividends further in the
future would increase from the $5.00 at a rate which depends on the economy. The current rate
long-term rate of interest is 6% per annum effective. Dividend increase rates are 4% per annum
effective in good times, 3% per annum effective in bad times. In the course of a few minutes,
news of a disastrous earthquake in Japan causes analysts to change their forecasts from ‘good’
to ‘bad’ economic times. Calculate the percentage drop in the UTSG stock price.
(A)
Less than 30.0000%
(B)
30.0000% but less than 31.0000%
(C)
31.0000% but less than 32.0000%
(D)
32.0000% but less than 33.0000%
(E)
33.0000% or more
10. (Assignment June 7, 2007) A loan of 10,000 is being repaid by a 30-year increasing
annuity-immediate. The initial payment is k, and each subsequent payment is k larger than the
preceding payment. Determine the principal outstanding immediately after the ninth payment,
using an annual effective interest rate of 4%.
(A) Less than 11,800.00
(B) 11,800.00 but less than 11,900.00
(C) 11,900.00 but less than 12,000.00
(D) 12,000.00 but less than 12,100.00
(E) 12,100.00 or more
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2007 TEST 2
11. (Assignment June 7, 2007) A loan of $15,117.05 is made with interest at a nominal annual
rate of 12% compounded monthly. The loan is to be repaid by 48 monthly payments starting
one month after the loan is made of $400 over 49 months, there being a repayment at the end of
each month but one. At the end of which month is the missing payment?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
12.(Lecture June 5, 2007) You and your spouse buy a house for $500,000, borrowing $400,000
in the form of a 25 year Canadian mortgage with an interest rate of 7% per annum compounded
semi-annually. Payments, as usual, are level at the end of each month. After 7 years you sell
the house, which has inflated at 5% per annum effective. On the sale you pay a real estate
commission of 4%, transfer tax of 1.25%, legal fees of $1,500 and zero mortgage prepayment
penalty. Calculate the amount of the ‘can spend this on champagne’ cheque which your lawyer
gives you after the sale is finalized
(A)
Less than $350,000.00
(B)
$350,000.00 but less than $355,000.00
(C)
$355,000.00 but less than $360,000.00
(D)
$360,000.00 but less than $365,000.00
(E)
$365,000.00 or more per annum
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2007 TEST 2
13.
For purposes of identifying your privacy ID, please code question 13 with the privacy ID
(A), (B), (C) or (D) indicated in the footer of this and every page.
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