Assignment 1
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School
Conestoga College *
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Course
SSC174
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
5
Uploaded by AdmiralTeam13438
Assignment 1 Solutions
Section A: Solve the following questions based on Simple and Compound Interest
Question 1
( 8.3 Question 10)
Sun Life Financial Trust offers a 360-day short-term GIC at 0.65%. It also offers a 120-day short-term GIC at 0.58%. You are considering either the 360-day GIC or three consecutive 120-day GICs. For the 120-day GICs, the entire maturity value would be "rolled over" into the next GIC. Assume that the posted rate increases by 0.1% upon each renewal. If you have $115,000 to invest, which option should you pursue and how much more interest will it earn?
Answer 1
Step 1: For the first GIC investment option, P = $115,000
r = 0.65% per year
t = 360 days For the second GIC investment option, Initial P = $115,000 r = 0.58% per year increasing 0.1% upon each renewal
t = 120 days each
Step 2: Transforming both time variables, t = 360
365
and t = 120
365
.
Step 3 (1st GIC option): S
1
= $115,000(1 + (0.0065)(
360
365
)) = $115,000 × 1.006410 = $115,737.26
Step 3 (2nd GIC option, 1st GIC): S
2
= $115,000(1 + (0.0058)(
120
365
)) = $115,000 × 1.001906 = $115,219.29
Step 3 (2nd GIC option, 2nd GIC): S
3
= $115,219.29(1 + (0.0068)(
120
365
)) = $115,219.29 × 1.002235 = $115,476.88
Step 3 (2nd GIC option, 3rd GIC): S
4
= $115,476.88(1 + (0.0078)(
120
365
)) = $115,476.88 × 1.002564 = $115,773.01
Amount better = $115,773.01 − $115,737.26 = $35.75
The 3 back-to-back GICs are better than the 360 day GIC by $35.75
MATH 10037-Assignment#1-Solution Page 1
of 5
Question 2 ( 9.4 Question 11)
Darwin is a young entrepreneur trying to keep his business afloat. He has missed two payments to a creditor. The first was for $3,485 seven months ago and the second was for $5,320 last month. Darwin has had discussions with his creditor, who is willing to accept $4,000 one month from now and a second payment in full six months from now.
If the agreed upon interest rate is 7.35% compounded monthly, what is the amount of the second payment?
Answer 2
Step 1: IY = 7.35%; CY = 12
Original Agreement: Payment 1 = $3,485 due 7 months ago
Payment 2 = $5,320 due 1 month ago
Proposed Agreement: Payment 1 = $4,000 due in 1 month
Payment 2 = $x due in six months
Step 2: Focal date = 6 months from today
Step 3: i = IY ÷ CY
i = 7.35% ÷ 12 = 0.6125% Step 4: N = CY × Years
Original Payment 1: N = 12 × 1
1
12
= 13
Original Payment 2: N = 12 × 7
12
= 7
Proposed Payment 1: N = 12 × 5
12
= 5
Proposed Payment 2: no need to move, already on focal date
Step 5: Original Payment 1: FV = $3,485(1+0.006125)
13
= $3,772.923571
MATH 10037-Assignment#1-Solution Page 2
of 5
Original Payment 2: FV = $5,320(1+0.006125)
7
= $5,552.329294
Proposed Payment 1: FV = $4,000(1+0.006125)
5
= $4,124.009845
Step 6: Original = Proposed
$3,772.923571 + $5,552.329294 = $4,124.009845 + x
$9,325.252865 = $4,124.009845 + x
x = $5,201.24
Section B: Solve the following based on Annuities Question 1 ( all are from chp 11 - 2, 8, 13)
Canseco wants to have enough money so that he could receive payments of $1,500 every month for the next nine-and-a half years. If the annuity can earn 6.1% compounded semi-annually, how much less money does he need if he takes his payments at the end of the month instead of at the beginning?
Answer 1
Step 1: General annuity due & Ordinary general annuity
Step 2: FV = $0; IY = 6.1%; CY = 2; PMT = $1,500; PY = 12; Years = 9.5
Step 3: i = IY ÷ CY = 6.1% ÷ 2 = 3.05%
Step 4: FV = $0, therefore skip
Step 5: N = PY × Years = 12 × 9.5 = 114 payments
PV
DUE
=
PMT
[
1
−
[
1
(
1
+
i
)
CY
PY
]
N
(
1
+
i
)
CY
PY
−
1
]
×
(
1
+
i
)
CY
PY
=
$
1,500
[
1
−
[
1
(
1
+
0.0305
)
2
12
]
114
(
1
+
0.0305
)
2
12
−
1
]
×
(
1
+
0.0305
)
2
12
PV
DUE
=
$
1,500
[
1
−
[
1
1.005019
]
114
0.005019
]
×
1.005019
=
$
1,500
[
0.434948
0.005019
]
×
1.0175
=
$
130,619.39
PV
ORD
=
PMT
[
1
−
[
1
(
1
+
i
)
CY
PY
]
N
(
1
+
i
)
CY
PY
−
1
]
=
$
1,500
[
1
−
[
1
(
1
+
0.0305
)
2
12
]
114
(
1
+
0.0305
)
2
12
−
1
]
PV
ORD
=
$
1,500
[
1
−
[
1
1.005019
]
114
0.005019
]
=
$
1,500
[
0.434948
0.005019
]
=
$
129,966.97
MATH 10037-Assignment#1-Solution Page 3
of 5
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Less = $130,619.39 − $129,966.97 = $652.42
Question 2
An investment fund has $7,500 in it today and is receiving contributions of $795 at the beginning of every quarter. If the fund can earn 3.8% compounded semi-annually for the first one-and-a-half years, followed by 4.35% compounded monthly for another one-and-three-quarter years, what will be the maturity value of the fund?
Answer 2
Step 1: General annuities due
Step 2: First Time Segment: PV = $7,500; IY = 3.8%; CY = 2; PMT = $795; PY = 4; Years = 1.5
Second Time Segment: PV = FV
1
; IY = 4.35%; CY = 12; PMT = $795; PY = 4; Years = 1.75
Time Segment 1:
Step 3: i = IY ÷ CY = 3.8% ÷ 2 = 1.9%
Step 4: N = CY × Years = 2 × 1.5 = 3 compounds
FV
1
= PV(1+i)
N
= $7,500 (1+0.019)
3
= $7,935.673943
Step 5: N = PY × Years = 4 × 1.5 = 6 payments
FV
DUE
1
=
PMT
[
[
(
1
+
i
)
CY
PY
]
N
−
1
(
1
+
i
)
CY
PY
−
1
]
×
(
1
+
i
)
CY
PY
=
$
795
[
[
(
1
+
0.019
)
2
4
]
6
−
1
(
1
+
0.019
)
2
4
−
1
]
×
(
1
+
0.019
)
2
4
FV
DUE
1
=
$
795
[
[
1.009455
]
6
−
1
0.009455
]
×
1.009455
=
$
795
[
0.058089
0.009455
]
×
1.009455
=
$
4,930.367496
Total FV
1
= $7,935.673943 + $4,930.367496 = $12,866.04144
Time Segment 2:
Step 3: i = IY ÷ CY = 4.35% ÷ 12 = 0.3625%
Step 4: N = CY × Years = 12 × 1.75 = 21 compounds
FV
2
= PV(1+i)
N
= $12,866.04144 (1+0.003625)
21
= $13,881.80167
MATH 10037-Assignment#1-Solution Page 4
of 5
Step 5: N = PY × Years = 4 × 1.75 = 7 payments
FV
DUE
2
=
PMT
[
[
(
1
+
i
)
CY
PY
]
N
−
1
(
1
+
i
)
CY
PY
−
1
]
×
(
1
+
i
)
CY
PY
=
$
795
[
[
(
1
+
0.003625
)
12
4
]
7
−
1
[
(
1
+
0.003625
)
12
4
]
−
1
]
×
(
1
+
0.003625
)
12
4
FV
DUE
2
=
$
795
[
[
1.010914
]
7
−
1
0.010914
]
×
1.010914
=
$
795
[
0.078948
0.010914
]
×
1.010914
=
$
5,813.332556
Total FV
2
= $13,881.80167 + $5,813.332556
Total FV
2
= $19,695.13
MATH 10037-Assignment#1-Solution Page 5
of 5