Family name, comma, personal name: _________________________________________
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UNIVERSITY OF TORONTO
ACT240H1F
ON-CHALKBOARD SICK CERTIFICATE TERM TEST 2 June 16, 2008
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: 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 code, please code question 11 with the privacy
code (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 2008 TEST 2
1. (Assignment May 29, 2008) A discount snowmobile store announces the following financing
arrangement:
“We don’t offer you confusing interest rates. We’ll divide your total cost by 10.7 and you can
pay us that amount each month for a year”
The first payment is due on the date of sale and the remaining eleven payments at monthly
intervals thereafter. Calculate the effective annual interest rate the store’s customers are paying
on their loans.
(A) Less than 20.000%
(B) 20.000% but less than 21.000%
(C) 21.000% but less than 22.000%
(D) 22.000% but less than 23.000%
(E) 23.000% or more
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2008 TEST 2
2. (Question of class, May 29, 2008) 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 8.5% per annum
interest effective.
Just after time 10 you withdraw all your money from all three banks. Calculate the total of your
withdrawals
(A)
(B)
(C)
(D)
(E)
Less than $167,000.00
$167,000.00 but less than $168,000.00
$168,000.00 but less than $169,000.00
$169,000.00 but less than $170,000.00
$170,000.00 or more
3. (Class) We amortize a $20,000 loan to buy a car, 4 years at 10% interest, payable at the end of
each year. Just after the 1st payment, the loan is renegotiated to be extended to 1+6 years (so the
last payment is at time 7). The interest rate used is the new market rate of 9.5% but the balance of
the old loan uses the initial 10%. Calculate the new annual payment
(A) Less than $3,400.000
(B) $3,400.000 but less than $3,500.000
(C) $3,500.000 but less than $3,600.000
(D) $3,600.000 but less than $3,700.000
(E) $3,700.000 or more
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2008 TEST 2
4.(Question of class May 27, 2008) 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 5.9% per annum effective. On the sale you pay a
real estate commission of 5.5%, transfer tax of 1.25%, legal fees of $2,000 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)
(B)
(C)
(D)
(E)
Less than $350,000.00
$350,000.00 but less than $355,000.00
$355,000.00 but less than $360,000.00
$360,000.00 but less than $365,000.00
$365,000.00 or more
5. (Tutorial June 3, 2008) Jan receives a 10-year increasing annuity-immediate paying 50 the first
year and increasing by 50 each year thereafter. Mary receives a 10-year decreasing annuityimmediate paying X the first year and decreasing by X/10 each year thereafter. At an effective
annual interest rate of 5%, both annuities have the same present value. Calculate X to the nearest
$10.
(A) 340
(B) 370
(C) 400
(D) 430
(E) The correct answer is not given by (A), (B), (C) or (D)
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2008 TEST 2
6. Payments of 25 each are made every 2 months from June 1, 2003 to April 1, 2009, inclusive.
Find, to the nearest $10, the value of the series 10 months before the first payment at a nominal
annual rate i(3) = 0.12.
(A)
(B)
(C)
(D)
(E)
$590
$610
$630
$650
The correct answer is not given by (A), (B), (C) or (D)
(
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2008 TEST 2
7. (Question of tutorial January 29, 2008) Ralph buys a perpetuity-due paying 500 annually. He
deposits the payments into a savings account earning interest at an annual effective rate of 9%.
Ten years later, before receiving the eleventh payment, Ralph sells the perpetuity based on an
effective annual interest rate of 9%. Using the proceeds from the sale plus the money in the
savings account, Ralph purchases an annuity-due paying X per year for 20 years at an effective
annual rate of 9%. Calculate X to the nearest $10.
(A) $1,320
(B) $1,360
(C) $1,400
(D) $1,440
(E) The correct answer is not given by (A), (B), (C) or (D)
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2008 TEST 2
8. A small business takes out a loan of 12,000 at a nominal rate of 8%, compounded quarterly, to
help finance its start-up costs.
Payments of 750 are made at the end of every 6 months for as long as is necessary to pay back the
loan.
Three months before the 9th payment is due, the company refinances the loan at a nominal rate of
12%, compounded monthly.
Under the refinanced loan, payments of R are to be made monthly, with the first monthly payment
to be made at the same time that the 9th payment under the old loan was to be made. A total of 25
monthly payments will completely pay off the loan.
Determine R.
(A)
(B)
(C)
(D)
(E)
less than 390
390 but less than 460
460 but less than 490
490 but less than 625
625 or more
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2008 TEST 2
9. A loan is paid off by level payments at the end of years one through five inclusive, hence the
outstanding balance OB5=0. You are given for year 1, where PR indicates principal repaid:
OB1 = $1412.00
I1 = $86.20
PR1 = $312
Calculate the outstanding balance OB3
$700
(A)
(B)
$720
(C)
$740
(D)
$760
(E)
$780
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UNIVERSITY OF TORONTO: ACT240H1F SUMMER 2008 TEST 2
10. You are given:
1. the present value of an annuity-due that pays 300 every 6 months during the first 15 years
and 200 every 6 months during the second 15 years is 6000;
2. the present value of a 15-year deferred annuity-due that pays 350 every 6 months for 15
years is 1580;
3. the present value of an annuity-due that pays 100 every 6 months during the first 15 years
and 200 every 6 months during the next 15 years is X.
The same interest rate is used in all calculations. Determine X
(A) 2302
(B) 2402
(C) 2502
(D) 2602
(E) 2702
11.
Please code question 11 with the privacy code (A), (B), (C) or (D) indicated in the footer
of this and every page.
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