CHS08 - General Mathematics
GBS FOR WEEK NO. 13 of 20
Supplementary Exercises
A. Complete the table by computing for unknown values. In numbers 3, 6, and 9, round
off your answer to six decimal places.
Nominal
Interest
Frequency
Interest Rate
Equivalent
Rate per
Rate
compounde
of
per Period
Nominal
period,
d
Conversion
Rate
based on
Periods
rate and
period
from
previous
column
10%
quarterly
(1)
(2)
___(3)_
(4)
compounde
d semiannually
6%
semi2
(5)
__(6)___
(7)
annually
compounde
d monthly
12%
monthly
12
(8)
__(9)___
(10)
compounde
d quarterly
1st row:
Nominal
Rate
Interest
compounded
Frequency
of
Conversion
Periods
10%
Quarterly
(3 months)
3
Interest Rate
per Period
0.1
4
=
Equivalent
Nominal
Rate
10.3812%
compounded
semiannually
Rate per
period,
based on
rate and
period
from
previous
column
10.3812
%
0.025 = 2.5%
Given: equal P; equal t
10% compounded quarterly
i(4) = 0.1
m=4
P
t
__% compounded semi-annually
i(2) = ?
m=2
P
t
Let F1 be the future value when interest is compounded semi-annually, and F 2 be the
future value when interest is 10% compounded quarterly.
F1 = F2
1+
1+
i (4 ) 4 t
¿
4
i (2 ) (2 )t
¿ =P ¿
2
P¿
0.1 4
¿
4
i (2 )
(1+ )=¿
2
1+
i(i) = (1.025)4 – 1
i(2) = 0.103812 = 10.3812%
Answer: 10.3812% compounded semi-annually
2nd row:
Nominal
Rate
Interest
compounded
Frequency
of
Conversion
Periods
Interest Rate
per Period
Equivalent
Nominal
Rate
Rate per
period,
based on
rate and
period
from
previous
column
6.09%
6%
Semi2
6.09%
0.06
compounded
annually
compounded
=
2
(6 months)
semimonthly
annually; i(2)
0.03 = 3%
= 0.06
Given: equal P; equal t
6% compounded semi-annually
i(2) = 0.06
m=2
P
t
(12)
__% compounded monthly
i
=?
m = 12
P
t
Let F1 be the future value when interest is compounded monthly, and F2 be the
future value when interest is 6% compounded semi-annually.
F1 = F2
(2 )
1+
i 2t
¿
2
i (12 ) (12) t
1+
¿ =P ¿
12
P¿
0 . 06 2
¿
2
i (12 )
(1+ )=¿
12
1+
i(i) = (1.03)2 – 1
i(12) = 0.0609 = 6.09%
Answer: 6.09% compounded monthly
3rd row:
Nominal
Interest
Frequency
Interest
Equivalent
Rate per
Rate
compounded
of
Conversion
Periods
12%
compounde
d monthly;
i(12) = 0.12
Monthly
(12 months)
12
Rate per
Period
0.12
12
=
Nominal Rate
12.6825%
compounded
quarterly
period,
based on
rate and
period
from
previous
column
12.6825
%
0.01 = 1%
Given: equal P; equal t
12% compounded monthly
i(12) = 0.12
m = 12
P
t
__% compounded quarterly
i(4) = ?
m=4
P
t
Let F1 be the future value when interest is compounded quarterly, and F2 be the
future value when interest is 12% compounded monthly.
F1 = F2
1+
1+
0.12 12 t
¿
12
i ( 4) ( 4 ) t
¿ =P ¿
4
P¿
0.12 12
¿
12
i ( 4)
(1+ )=¿
4
1+
i(i) = (1.01)12 – 1
i(4) = 0.126825 = 12.6825%
Answer: 12.6825% compounded monthly
B. Complete the table by finding the unknown time and rate.
1st row:
1
1.5917%
Quarterly
8,000
0.3979
%
0.7974
%
1.1985
%
1.6012
%
2.0055
%
2.4114
%
2.8189
%
3.2281
%
3.6389
%
4.0513
%
4.4653
%
4.881%
1
2
3
5.2984
%
5.7174
%
6.138%
2
3
6.5604
%
6.9844
%
7.4101
%
7.8375
%
8.2667
%
8.6975
%
9.13%
9.5643
%
10.0003
%
4
5
6
1
31.83
2
63.79
3
95.88
4
128.1
5
160.44
6
192.91
7
225.52
8
258.25
9
291.11
10
324.1
11
357.22
12
390.48
13
423.87
14
457.39
15
491.04
16
524.83
17
558.75
18
592.81
19
627
20
661.33
21
695.8
22
23
730.4
765.14
24
800.02
8,031.8
3
8,063.7
9
8,095.8
8
8,128.1
8,160.4
4
8,192.9
1
8,225.5
2
8,258.2
5
8,291.1
1
8,324.1
8,357.2
2
8,390.4
8
8,423.8
7
8,457.3
9
8,491.0
4
8,524.8
3
8,558.7
5
8,592.8
1
8,627
8,661.3
3
8,695.8
8,730.4
8,765.1
4
8,800.0
2
2nd row:
11%
Semi75,000
annually
1
2
5.5%
11.3025
%
17.4241
%
23.8825
%
30.696%
37.8843
%
45.4679
%
53.4687
%
61.9094
%
70.8144
%
80.2092
%
90.1207
%
100.577
4%
111.609
1%
123.247
6%
135.526
3%
1
1
2
3
2
4
3
5
6
7
4
8
9
5
10
11
6
12
13
7
14
15
8
16
4,125
8,476.8
8
13,068.
1
17,911.
85
23,022
28,413.
21
34,100.
94
40,101.
49
46,432.
07
53,110.
83
60,156.
93
67,590.
56
75,433.
04
83,706.
86
92,435.
74
101,64
4.7
79,125
83,476.8
8
88,068.1
92,911.8
5
98,022
103,413.
21
109,100.
94
115,101.
49
121,432.
07
128,110.
83
135,156.
93
142,590.
56
150,433.
04
158,706.
86
167,435.
74
176,644.
7
C. Solve the following problems:
21. Jun invested an amount of ₱100,000 where he obtained an interest of ₱16,000 at the
end of 2 ½ years. At what nominal rate compounded semi-annually was it invested?
Given: F = ₱100,000
P = ₱16,000
t = 2.5 years
m=2
n = mt = (2)(2.5) = 5
Find: i(2)
Solution:
F = P(1+j)n
100,000 = 16,000 (1 + j)5
5
1+ j ¿
100000
=¿
16000
1+ j¿5
6.25=¿
1
5
6.25 ¿ =1+ j
¿
1
6.25 ¿ 5 −1=0.4426
¿
j=0.4426
i
(¿¿ 2)
m
j=¿
i
(¿¿ 2)
2
0.4426=¿
i(2) = (0.4426)(2)
i(2) = 0.8852 or 88.52%
22.Jen invested an amount of ₱400,000 at 5% compounded quarterly. How long
should she let the investment stay if she wants to earn ₱50,000?
i(4 ) 0.12
Given :F =400,000 P=50,000 i =0.12 m=4 j= =
=0.03
m
4
(4 )
Find: t
Solution:
F = P(1+j)n
400,000 = 50,000(1 + 0.03)n
log
=n log(1.03)
( 400,000
50,000 )
400000
)
50000
n=
=70.3493 periods
log(1.03)
log(
n 70.3493
t= =
=17.58 year s
m
4
23. Mr. Retanan was given a loan at 10% compounded monthly. When should he pay it
so that it will just earn only 10% of the amount borrowed?
( 12 )
Given :i( c )=0.1 P F=1.2 P i =0.1 m=12 j=
i(12) 0.1
= =0.0083333333333333 0.008333
m 12
Find: t
Solution:
F = P(1+j)n
1.2P = P(1 + 0.008333)n
1.2 = (1.008333)n
log(1.2) = log(1.008333)n
log(1.2) = n log1.008333)
n=
log 1.2
=21.97 periods
log(1.008333)
n 21.97
t= =
=5.49 year s
m
4
24.At what interest rate compounded quarterly should an amount be invested
if the interest earned is 20% of the invested amount for 5 years?
25.What simple interest rate is equivalent to 1% compounded quarterly?
(4)
Given :i =0. 01m=4 t=5 years
Find: r
Solution:
Simple Interest
Compound Interest
Fs
P ( 1+ r s t )
=
( 1+r s t )
=
1+
4
(i) 4 t
1+
¿
4
¿
=
Substitute t = 5
(1+r s )
(1+r s )
rs
Fc
=
=
=
1+
1+
= 0.0100 or 1%
(i)4 4
¿
4
¿
0.01 4
¿
4
¿
(i)4 4 t
¿
m
P¿