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Midterm

# ADMS 3530_Winter 2012_midterm exam solutions.pdf

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York University

Administrative Studies

ADMS 3530

Irvin Pestano

Fall

Description

Name Section ID #
Prof. Sam Alagurajah Section M Thursdays 4:00 – 7:00 PM
Prof. Lois King Section N Tuesdays, 7:00 – 10:00 PM
Prof. Lois King Section O Internet
Prof. Lois King Section P Mondays 11:30 – 2:30 PM
Prof. Irvin Pestano Section Q Wednesdays, 7:00 – 10:00 PM
Prof. Kwok Ho Section R Fridays, 2:30 – 5:30 PM
Prof. Dayna Patterson Section S Mondays, 2:30 – 5:30 PM
Prof. Muz Parkhani Section T Thursdays 7:00 – 10:00 PM
ADMS 3530.03 Finance Midterm Exam
Winter 2012
Saturday Feb. 11, 2012
Type A Exam
This exam consists of 30 multiple choice questions and is worth a total of 100 marks.
Choose the response which best answers each question. Circle your answer below, and
fill in your answers on the bubble sheet. Only the bubble sheet is used to determine
your exam score. Please do not forget to write your name and ID # both at the top of this
cover page and on the bubble sheet. Also, please write the type of your exam (A or B) on
the bubble sheet.
Please note the following:
1) Read the questions carefully and use your time efficiently.
2) Choose the answers that are closest to yours because of possible rounding.
3) Keep at least 4 decimal places in your calculations and final answers and at least 6
decimal places for the interest rate.
4) Each question is worth one (1) mark.
5) Unless otherwise stated, interest rates are expressed on an annual basis, and
bonds pay semi-annual coupons and have a face value (or par value) of $1,000.
6) You may use the back of the exam paper as your scrap paper.
7) We will NOT answer any questions during the exam.
1 Numerical Questions
1. Ms. Yumi Masui plans to make the following annual contributions to her investment
account for the next 34 years:
Year Amount ($)
1 8,000
2 4,000
3 5,000
4 7,000
5 3,000
6 and thereafter 9,000 per year
If the contributions are made at the end of each year, and the rate of interest is 5%, how
much money will she have at the end of 34 years?
A) $719,545.98
B) $650,000.72
C) $475,527.50
D) $685,281.88
E) $691,500.75
Answer: D
She will have $8,000 (1.05)33+ $4,000 (1.05)32+ $5,000 (1.05)31 + $7,000 (1.05)30
$3,000 (1.05) + ($9,000) FVIFA(5%, 29 years)
+
= $124,377.48 + $560,904.40 = $685,281.88
2. Gerard and Daniele Lang are buying a house and will require a mortgage of $150,000.
The rate is 6.85% for a 10-year term, repayable in equal monthly payments. They want to pay
down the mortgage quickly, but they also don’t want to “be slaves to their mortgage”.
Therefore, they have agreed on a 20-year amortization. What will be the principal owing when
the mortgage comes up for renewal in ten years?
A) $99,343.99
B) $136,477.93
C) $99,662.94
D) $90,678.61
E) $127,728.53
Answer: A
The effective annual rate on the mortgage
2
EAR = (1 + (0.0685/2)) – 1 = 6.9673…%
The equivalent monthly rate,Mon= 0.005628535…or 0.5628535...%
The monthly payment on the mortgage
PV = 150,000; N = 240; I/P=r = 0.005628535…or 0.5628535...%; PMT = $1,140.92
Mon
2 The principal owing when the mortgage comes up for renewal in ten years
N=120; I/P= r = 0.005628535…or 0.5628535...%; PMT=1,140.92; PV= 99,343.99
Mon
3. Victor Wong recently graduated from business school and has just started working as a
marketing analyst. He has decided that he needs more reliable and fun transportation. He
has decided to get a Volkswagen for $30,000, plus sales taxes of 13%. What will be the
monthly payments if he buys the car with a $5,000 down payment and with a 48-month loan
based on a 4.8% APR rate?
A) $660.29
B) $662.93
C) $648.02
D) $588.54
E) $709.94
Answer: B
PV=($30,000)(1.13) – 5,000 = 28,900; N = 48; I/P = 0.4%; PMT = 662.93
4. Dave deposits $2,500 in a 4-year term deposit that pays 4% interest with quarterly
compounding. At the end of four years, he transfers the amount to a 3-year term deposit
that pays 5% interest with daily compounding. How much will he have at the end of 7
years?
A) $3,385.64
B) $1,953.26
C) $3,405.82
D) $2,932.65
E) $3,011.57
Answer: C
He will have $2,500 (1+.04/4) 16(1+.05/365) (3)(365= $3,405.82
5. Jonathan has just signed a contract to buy a boat. The manufacturer gives him five
options of payment:-
(I) $4,600 per year, at the end of each year, for 5 years.
(II) $4,200 per year at the beginning of each year for 6 years.
(III)$6,000 at the beginning of each year for 4 years.
(IV) $3,000 at the end of year 1, $2,000 at the end of year 2, 18,000 at the beginning
of year 5.
(V)$20,000 now
If the rate of interest is 6%, which option is the best for him?
3 A) I
B) II
C) III
D) IV
E) V
Answer: D
PV(I) = ($4,600) PVIFA(6%, 5years) = $19,376.87
PV(II) = ($4,200) PVIFAD(6%,6years) = $21,891.93
PV(III) = ($6,000) PVIFAD(6%,4years) = $22,038.07
PV(IV) = 3,000 (1.06) -1+ $2,000 (1.06) -+ $18,000 (1.06) = $18,867.86
PV(V) = $20,000
Therefore, option IV is the best for him.
6. The current balance in your RRSP account is $120,000 and you want to retire in 30
years with $1,500,000. If you save $8,000 annually at the end of each year, what interest
rate do you need to earn in order to reach your goal?
A) 6.54%
B) 7.75%
C) 8.12%
D) 9.37%
E) 9.44%
Answer: A
The FV of the 30 payments and the $120,000 must be $1,500,000, or:
FV = 1,500,000 = 8,000 x FVIFA(r,30) + 120,000 x (1+r)30
(In your calculator: PV = 120,000 ; PMT = 8,000 ; FV = -1,500,000 ; n = 30)
Solving for r, we find r = 6.54%
7. You are planning to establish a 30-year scholarship fund that will be given to
economically disadvantaged students who have made a difference in their communities.
The scholarship will pay $30,000 at the end of the first year and then increase by 2.5% per
year. If you expect that the fund will earn a 6% annual rate of return, how much should you
donate today in order to maintain this scholarship?
A) $544,108
B) $581,214
C) $812,593
D) $857,143
E) $929,675
Answer: A
4 PV of a growing annuity (the growth rate g = 2.5%) is given by:
t
C1 1 g
PV of a declining annuity = r g 1 r
30
= 30,000 10.025
0.06(0.025) 1.06
= $857,142.8571 X 0.6348 = $544,108
8. You are indifferent between the following two payment options: 1) pay $22,000 cash
today, or 2) pay $400 monthly over the next 2 years with the first payment starting
immediately, plus a final payment ($FP) to be made 3 years from today. An APR of 8.4% is
quoted with monthly compounding. How much is FP?
A) $9,456.06
B) $9,494.60
C) $12,155.45
D) $16,877.78
E) $16, 957.05
Answer : D
rm= 8.4%/12 = 0.70% 36
22,000 = $400 (1.007) x PVIFA(24, 0.7%) + FP/ (1.007 )
FP = (22,000 - $8,870.3039) X (1.007 ) 36
FP = $16,877.78
9. Which account would be preferred by a borrower: a 6% APR with monthly compounding
or an 6.2% APR with semiannual compounding?
A) 6% with monthly compounding.
B) 6.2% with semiannual compounding.
C) The borrower would be indifferent.
D) The time period must be known in order to select the preferred account.
E) None of the above.
Answer: A
The EAR corresponding to an 6% APR with monthly compounding =
(1 + (6% /12)) - 1 = 6.17%
The EAR corresponding to an 6.2% APR with semiannual compounding =
(1+(6.2%/2)) - 1 = 6.30%.
10. How much are you willing to pay for a perpetual monthly income growing at 0.75% per
month and starting today at $1,000 if the interest rate is 10%?
5 A) $960,000
B) $975,253
C) $1,200,480
D) $1,210,484
E) Infinity
Answer: D
It is a PV of a growing perpetuity due problem.
im = 10%/12 = 0.583333%
PV = 1,000 x (1+0.83333%) / (0.83333% - 0.75%) = $1,210,484
11. Today Shaniqua purchased a bond at a price of $987 per $1,000 of face value. The
bond matures in five years, pays semi-annual interest, and has a 6.5% coupon rate. If she
holds the bond to maturity, what real rate of return will she earn if inflation remains constant
at 2%?
A) 6.52%
B) 4.72%
C) 6.72%
D) 6.81%
E) 4.81%
Answer: B
Using your calculator
Price = PV = $987; FV = $1,000; N = 5 x 2 = 10; Coupon = PMT = $65 / 2 = $32.50; Solve
for I/Y = 3.4056% which is the 6 month rate, the YTM is an annualized rate = 3.4056% x 2
= 6.8111% which is a nominal rate
Real rate of return = [(1 + nominal rate) / ( 1 + inflatio

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