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Unformatted text preview: ACTSC 231 Fall 2009 1. [7 marks] Suppose your bank account earns 5% annual effective interest if the balance is less than $1000, and 5.5% otherwise. You invest $907.03 on Dot 6, 2009. (a) [3 marks] Find the accumulated value on January 18, 2012, using 1. exact simple interest @0117: (glosf: {30:24.03 ~» Dar 6, Port.
actor? : 25 + 39 + 31 vi 153 :10“!
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ii. ordinary simple interest
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A\l= 1000005'5Wi : truisrza (b) [2 marks] Now assuming that the bank credits you simple interest for fractional parts of a year, ﬁnd the value using ‘1. exact simple interest :/\\f : [0:90 (1 + 0. 053‘ x ’g’jj] :. $10] 3 [(2%
ii. Bankers’ rule . [on] . _0 I W 0
Av: \QOD(l+ 0093*;12) 1’ itmmﬁﬂ (c) [2 marks] Find the present value of $1500 due at time t = 10 years. [FIVE] j: Scclx that] $[QCC : . lo (1,?) 5 :— ;] k 3) bye(S
loj(l~0‘§’) Them 'qu [VOW] . 2,.‘127
5131000 (5, I“ : a; $861?) 3 {[1000 ban]: 2 fl L] 54ch * ML 306/0 ACTSC 231 Fall 2009 2. [8 marks] The accumulation function for an investment is 0,05) = b + at + 0.01252. (a) [1 mark] Find b. 01:0] :] (A
O (b) [3 marks] Given that the effective rate of interest i2 = 5.77%, ﬁnd 0. l2 3' 052/] Ram] __ [b+ 2C + 0434] ~ <5 “t c 't Grew]
m(\i * «m ~um i ~M ....... t m wars
5 ‘t ( + U U]
: C. +03}: M
TOM, ~ 0406.74
Slolv‘iv/WB / C, 2 x (c) [2 marks] Find the force of interest (5t. You can leave (2 in your expression. w — . C.'+ U <>24t
0(47 é~w~w~fﬁm_ ........ "at
K ] [’3 ‘l' C]: "l Glad] Z ~’(e
are.) (d) [2 marks] What does this force tell us about the long term growth of this in— vestment compared to 5.77% compound interest? Explain in 1—2 sentences.
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"\ V\23r/W\€. 3' ‘l ( which i s COLAV‘S’kCA/vk'l‘ r Ck l he! ‘]‘/[\L7«L, (X10 WQCKjl "(hr CRAB ACTSC 231 Fall 2009 3. [5 marks] Organize the following 5 items into order from smallest to largest. You do not necessarily need to calculate them all, but justify your answer.
(a) The nominal interest rate convertible monthly (i(12)) that is equivalent to z' =
12% annual effective. (b) The real rate of return over one year if the annual effective interest rate is 14% and the CPI values are Q(0) = 102.0 and Q(1) = 104.8. (c) The annual effective rate of discount d that is equivalent to 11% nominal interest convertible quarterly (214)). (d) The nominal discount rate convertible semiannually (dm) that is equivalent to 2' = 12% annual effective. (e) The force of interest 6 that is equivalent to 11% nominal interest convertible quarterly (WU).
Write the letters (a, b, c, d, e) in order here: (C) < < 1;) < (45> < Justify your answer below (calculations and/ or explanations): CM Cl : /ll/‘Q.y> (N. iUCk, “1‘0 .ﬂkt SCH/ma FOR S O A (1) < (A2,) ‘ < ( (A A) ( cc)
COMO o,me {Cl 0M CK <51 WLOI'lV) / Cl < / g H /r
\ (k l ((4 ) C(ﬁcqlcgivu) (l3): \[Qiq : 1' 2 ‘ Deg 80 ) : L (“W”) ‘ V (C ClS‘f/J [1‘ (“,1 i 021‘15
.‘ 3715 , — i . . 06,4 . ..
COACKAQ \M/ (a ‘ B 15 39c l/L 67,; '1 (l ‘i’ 97/ ; 1. {HM
B: lbigj 0/0 50 (C) < (a) ((5). I (we Amrin mud (c) LA H‘g 10.23" 3%)
CQlCUlQTM) (M : cl”) is stalk 41"le 1+ 12%. :. (l * 3r ‘
a“’:\\.bi<r°/o 3; (av (a><mi (W don‘l' Med M M \l/lS H.277? > ...
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 Fall '09
 Chisholm

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