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Unformatted text preview: ~. ":VERSIONCODE T3 Your name: in format family name, comma; personal name(s): Your student ID:
5 UNIVERSITY OF TORONTO
‘ Faculty of Arts and Science
DECEMBER 20072EXAMINATIONS W
ACT230H1F 1,3559 ~
Duration — 2 Hours 9
. Instructor: Andrei Badescu, PhD
NOTES:
1. . Nonprogrammable calculators allowed
2 Scrap paper istobeehanded in With this book. 'Itﬁs OK to ’Write on book.
3. This is a closed book exam.
4. Multiple choice: :only Your letter answer mark sense sheet "will be graded.
5. Each question: 10 points correct; two if blank, zero points'if wrong
6. So expectation if you guessiis the same as leaving a'blank.
7. Timing: 120 minutes .
8. Make sureyou’ve indic'ated'your letter answers on the mark' sense sheet before time’s up
9. "  Please stay in your seats anddon’t talk till all question papers and mark sense sheets have been collected.
310. ‘ ' [Photo ID en desk during exam please.
11. = Name and student ID ‘on this question paper and on mark sense sheet please. 12. Please answer question 21~with version codes (T1, T2, or T3).
13. Good luck! UNIVERSITY OF TORONTO: ACT230H1F FALL 2007 FINAL VERSION CODE T3 1. A 10year loan of 2000 is to be repaid with payments at the end of each year. It can be repaid
under the following two options:
(i) Equal annual payments at an annual effective rate of 8.07%.
(ii) Installments of 200 each year plus interest on the unpaid balance at an annual effective
rate of i .
The sum of the payments under option (i) equals the sum of the payments under option (ii).
Determine i. (A) 8.75%
(B) 9.00%
(C) 9.25%
(D) 9.50%
(E) 9.75% 2. A loan is being repaid by 2n level payments, starting one year after the loan. Just after the nth
payment the borrower ﬁnds that she still owes 3/: of the original amount. What proportion of
the next payment is interest? (A) 1/3
(B) 2/3
(C) 1/2
(D) 1/4
(E) 1/6 rnnf’rl UNIVERSITY OF TORONTO: ACT230H1F FALL 2007 FINAL VERSION CODE T3 3. Jenny’s salary increases by 6% at the beginning of each year of work. She works for 30 years,
paying at each yearend a proportion Z of her earnings to a retirement fund which earns 6%
per annum taxfree. In her last year she earns $X. She draws at the end of her ﬁrst year of
retirement a pension of l .04X (1 —Z). The pension continues to increase for inﬂation at 4%
every year till the money runs out after 20 years of retirement. Calculate Z as a percentage
of earnings. (A) Less than 35.000% (B) 35.000% but less than 36.000%
(C) 36.000% but less than 37.000%
(D) 37.000% but less than 38.000%
(E) 38.000% or more 4. (FM manual, Section 6, Q1) A 20year annuity pays 100 every other year beginning at the
end of the second year, with additional payments of 300 each at the ends of years 3, 9 and 15.
The effective annual interest rate is 3%. Calculate the present value of the annuity. (A) Less than $1,470.000 (B) $1 ,470.000 but less than $1 ,480.000
(C) $1 ,480.000 but less than $1,490,000
(D) $1 ,490.000 but less than $1 ,500.000
(E) $1 ,500.000 or more 5. A loan is being repaid with level payments of K each made every 6 months. The outstanding
balances at three consecutive payment dates are 5,190.72, 5,084.68 and 4,973.66. What is the
payment amount K to the nearest dollar? A) 344
B) 346
C) 348
D) 350
E) 352 eont’r’ UNIVERSITY OF TORONTO: ACT230H1F FALL 2007 FINAL VERSION CODE T3 6. (FM manual, Section 9, Q8) A 2,000 loan is to be repaid with equal payments at the end of
each year for 20 years. The principal portion of the 13th payment is 1.3 times the principal
portion of the 5th payment. Calculate the total amount of interest paid on the loan . (A)Less than $770000
(B)$770.000 but less than $780,000
(C)$780.000 but less than $790000
(D)$800.000 but less than $810000
(E)$810.000 or more 7. (FM manual, Section 8, Q8) Gloria borrows 100,000 to be repaid over 30 years. You are
given: (i) Her ﬁrst payment is X at the end of year 1. (ii) Her payments increase at the rate of 100 per year for the next 19 years and remain level for
the following 10 years. (iii) The effective rate of interest is 5% per annum. Calculate X. A) 5105
B) 5205
C) 5305
D) 5405
E) 5505 8. Find the price of a $1000 par value 10year bond with coupons at 8.4% convertible
semiannually, which will be redeemed at $1050. The bond is bought to yield 10% convertible
semiannually. Calculate to the closest possible value. (A) 899
(B) 904
(C) 909
(D) 914
(E) 919 UNIVERSITY OF TORONTO: ACT230H1F FALL 2007 FINAL VERSION CODE T3 9. A 1000 par value bond with coupons at 9% payable semiannually was called for 1100 prior to
maturity. The bond was bought for 918 immediately after a coupon payment and was held to
call. The nominal yield rate convertible semiannually was 10%. Calculate the number of
years the bond was held. (AHO
(mzs
(039
0349
(E)54 10. (FM manual, Section 12, Q4) A 1000 par value 10year bond with semiannual coupons and
redeemable at 1100 is purchased at 1135 to yield 12% convertible semiannually. The ﬁrst
coupon is X. Each subsequent coupon is 4% greater that the preceding coupon. Determine X. omso
(m60
(Q70
anso
(B90 conPd., UNIVERSITY OF TORONTO: ACT230H1F FALL 2007 FINAL VERSION CODE T3 1 1. (FM manual, Section 10, Q3) Joe repays a loan of 10,000 by establishing a sinking fund and
making 20 equal payments at the end of each year. The sinking fund earns 7% effective
annually. Immediately after the ﬁfth payment, the yield on the sinking fund increases to 8%
effective annually. At that time Joe adjusts his sinking fund payment to X so that the sinking
fund will accumulate to 10,000 20 years after the original loan date. Determine X to the closest
possible value. A) 195
B) 200
C) 205
D) 210
E) 215 12. A 20 year immediate annuity is payable monthly. Immediate after the 43rd payment has been
made, the present value of the remaining annuity payments is calculated to be X. N is the
number of payments after which the present value of the remaining annuity payments is less than X/2 for the ﬁrst time. You are given d“) =0.08. Find N. A) 171
B) 172
C) 173
D) 174
E) 175 ﬁnstile? UNIVERSITY OF TORONTO: ACT230H1F FALL 2007 FINAL VERSION CODE T3 13. (FM manual, Section 1, Q1) 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 (i5%). 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 three years, if the annual effective
rate of interest were (i+9%) for each of the three years? A) 16,851
B) 17,196
C) 17,499
D) 17,936
E) 18,] 13 14. (FM manual, Section 2, Q2) You are given:
(i) Fund X accumulates at an interest rate of 8% compounded quarterly;
(ii) Fund Y accumulates at an interest rate of 6% compounded semiannually;
(iii) at the end of 10 years, the total amount in the two funds combined is 1000; and
(iv) at the end of 5 years the amount in Fund X is twice that in Fund Y.
Calculate to the nearest dollar the amount X(0) in fund X at time 0. (A) 302
(B) 307
(C) 312
(D) 319
(E) The correct answer is not given by (A), (B), (C) or. (D) confer , , UNIVERSITY OF TORONTO: ACT230H1F FALL 2007 FINAL VERSION CODE T3 15. (FM manual, Section 3, Q1) You are given a loan on which interest is charged over a 3year
period, as follows:
(i) an effective rate of discount of 8% for the ﬁrst year;
(ii) a nominal rate of interest of 5% compounded semiannually for the second year; and
(iii) a force of interest of 4% for the third year.
Calculate the annual effective rate of interest over the 3year period. (A) Less than 5.9000% (B) 5.9000% but less than 6.0000%
(C) 6.0000% but less than 6.1000%
(D) 6.1000% but less than 6.2000%
(E) 6.2000% or more 16. (FM manual, Section 3, Q7) The present value of $K due in 4 years is 678.80. If the force of
discount (same as force of interest 5) is cut by a factor of 1/5, that present value would be
766.30. What would the present value be if the rate of discount d is cut by a factor of 1/3?
Answer to the nearest $10. M)MO
(msw
(C)860
(D)870
(E)890 Ennnfd.” UNIVERSITY OF TORONTO: ACT230H1F FALL 2007 FINAL VERSION CODE T3
17. The force of interest is given by
5, = 0.]/(]+0.1t) t>0 At time zero you have $10,000. During the first year you earn interest of X. During the third
year you earn interest of Z. CalculateZX (A) Less than $100.00 (B) $100.00 but less than $200.00
(C) $200.00 but less than $300.00
(D) $300.00 but less than $400.00
(E) $400.00 or more 18. You buy a $400,000 house on January 1, 2008 and arrange with CitiBank a US. mortgage
amortized with level payments at the end of each month over a period with last payment
January 1, 2033. The interest rate is 6% per annum compounded monthly. Just after 24
payments have been made, you reﬁnance (pay off Citi) by borrowing the outstanding balance
from Chemical Bank at a rate of 3% per annum compounded monthly. The new mortgage is
amortized over a period with last payment January 1, 2033. Calculate the reduction in your
monthly mortgage payment. (A) Less than $575000 (B) $575000 but less than $600000
(C) $600000 but less than $625000
(D) $625000 but less than $650,000
(E) $650000 or more 19. A perpetuity is payable continuously at the annual rate of 1+t2 at time t. If the force of
interest is equal to 0.05, ﬁnd the present value of the perpetuity.
(A) 16000
(B) 16020
(C) 16040
(D) 16060
(E) 16080 r. ans1’?” (i UNIVERSITY OF TORONTO: ACT230H1F FALL 2007 FINAL VERSION CODE T3 20. (F M manual, Section 4, Q4) Sam deposits 1000 every year on his birthday into a retirement
fund earning an annual effective rate of 12%. The ﬁrst deposit is made on his 39th birthday
and the last deposit is made on his 60th birthday. Immediately after the last deposit, the
accumulated value of the ﬁmd is transferred. Calculate that accumulated value X. (A) Less than $90, 000 000 (B) $90, 000. 000 but less than $91, 000. 000
(C) $91, 000. 000 but less than $92, 000 000
(D) $92,000.000 but less than $93,000.000
(E) $93,000.000 or more 21 .If not already done, please identifying your version code test Tl , T2 or T3 answer question
21 as follows: (A) If you have version code Tl (B) If you have version code T2
(C) If you have version code T3 Total marks:200 (20 questions) ...
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