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Unformatted text preview: UWlD Number Problem 1. Multiple Choice questions. For each of the following questions, select the gn_e_ corred response by
circling the letter. 1.1 [3 marks] Interest is at rate i per period, with i > 0. The number of periods is N, and N>1t
(a) (F/A, l, N) < (FIA, 0, N) ,
/ lg 4,. (b) (AIP, i, N) > (NP, 0, N).
(c) (PIA, i, N) > (PIA, O, N) t
(d) (A/F.i,N)=1lN-i .
(e) The limit of (AIF, i, N) as N goes to inﬁnity is i . 1.2 [3 marks] A deposit of $250,000 hasjust been made into an account that earns interest at 4% per year,
compounded annually. Withdrawals of $5000 will be taken from the account each year, for 10 years, starting
one year from now, Further withdrawals of X dollars will be made every 5 years, forever, starting 5 years from
now Which of the following correctly calculates how large X can be? \/0L 4,. (a) (250,000 — 5000(P/A,4%,10)] x((1+.04)5-1} .
(b) (250.000 — 5000(PIA,4%,10)) x004 x5 .
(c) (250,000 + 5000(P/A,4%,10)) x((1+,04)5-1}t
(d) (250,000 — 5000(P/A,4%,10)) +((1+.04)5-1} ‘
(e) (250,000 + 5000(PIA,4%,10)) +((1+lo4)5-1) . Problem 2. [10 marks] A new coffee maker for your ofﬁce costs $100 now, and the costs of electricity. coffee grounds, milk and sugar will be $20 per month in the first month, then increasing by $0.10 per month each month compared to the previous month Calculate the present worth of these costs over 5 years, using a nominal interest rate of 12% per year, with monthly compounding. I MONK
' M “I t M l.: /i% ll :Mmﬁ/y eﬂeu‘ivﬁ Inﬁnjfruft 7": 66 I! P- I00 +£2.0-r o-Io(A/6 , l'/. ) éojjUZ‘, 12160) P; [00 + [£0 +0-lx £6633] X 44-755: “la”???
Zma/ILJ 2 mark: .4, mil/KS [oo UW ID Number Problem 3. [14 marks] Sam plans to deposit X dollars into an account earning 10% interest per year, each year for 6 years. starting
one year from now. to save for his son's university education, and for his son‘s ﬁrst car. Sam wants to save
enough that he can withdraw $8000 each year for 4 years for his son's education, in years 7, 8, 9, and 10 from
now, and also withdraw an extra $10.000 for a car 11 years from now, (a) Draw a rough cash ﬂow diagram to represent the deposits and the withdrawals. x szan'ﬁ
/ mark aAC/t WI'fkd/mwa/ 0V 0/9790-1/1" 0’1 call: fe/vw (mark Coy/(cf (JIII/QC'IT’O”) 0/ ouﬁ flow (b) Calculate the value 01 X, the amount of each ol the 6 deposits. Use interest factor symbols in your answer. 2 mark) 2 mar/<5 X §000(Z’/07‘14)+10000(&F #07057 g M
(I; nobé) 542301;.46 w 2mm“:
W 2 Mark! Caner/1’ e7w°frn” UWID Number Problem 4. A proposal to produce and sell a new children‘s toy is under consideration. The ﬁrst cost of equipment in the
factory would be $5 million now. the salvage value of the equipment would be 3 0.35 million in 8 years, the
annual operating costs would be 5 0.60 million in the ﬁrst year, and the annual operating costs would increase
by $ 0.05 million per year each year oompared to the previous year. It is expected that 0.5 million toys would
be sold each year for 8 years. at a price that starts at $15 per toy in the ﬁrst year, and decreases by 5% per
year each year compared to the previous year. The MARR = 9% per year. Write an expression involving the above data, and interest factor symbols, that would give the overall present
worth of the proposed investment. See page 1 for the list of allowed interest factor symbols. Do not evaluate
the expression, as the arithmetic will just take a lot of time. 0:35 i 0.5xlS [fl/mark;
I“)- [4-]. —‘= “I 3 1+; 1,0,05— 6ma’k:
Zmarks E WP Q 8
PW: ——5- [6.6'+0‘05-(’%2 7526)](éi 9/.) ) é man/k; + oJxIYUD/A) "15%) 3/(I— 0.05) 4. 0.35 C P/,: 2 7X) Lmur/CS ...
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- Winter '09
- Annual operating costs, factor symbols