買二第張六第日八初月一十年酉己愛 WAH KIU YAT PO
郭日僑平
二期里:日六十月二十年九六九一間公年八十五國民華中 育 汝僑華
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RO英文中學會考試題預習專欄
數
堅道英文書院主編
科
(E)
MATHEMATICS (7)
Simple and Compound Interest
Any money lent or borrowed is called the Principal and the churge made for its usa 19 called the interest and depends on how much has been borrowed and the length of time for which it is borrowed.
Interest is usually paid at fixed intervals, yearly, half-yearly or quarterly, and in this case tho principal is said to be lent at simple interest. If. the simple interest for a
any given time is added to the principal, the sum is called the amount at simple interest for that time.
nsactions
In transactions where the intersst as it falls due 18 not paid to the lender but is added on to, 1.8. compounded with, the principal, the money is said to be lent at compound interest, and the total sum owed after any given time is called the amount at compound interest for that time; the difference between the amount and the original principal is called the compound interest,
Formulae í If P is the principal in s“
Ria the rate of interest in % Tis the length of time in years
$ 18 the interest of SP.
SA 19 the amount of SP in 7 years
Then the simple interest $I - SP.R.T.
The compound
here
P.R.T
in which, the multiplying factor (R) } 18 called
growth factor if it is greater than otherwise is called a decay factor.
Example 1
A certain sum of money at compound interest amounts in two years to $800, and in three years to 8832. Find the sum of money
Let R be the rate of interest on the principal pr. Then in 2 yr. the amount 800 P(18)2
in 3 yr. the ♦ amount 832 • P(1 • R). Eat.(b) divided by qt.(a)
(a) (b)
If Cl amount to £2 in n yr
(1.04) 2.
a log 1.04 = log 2
0.3010 0.01703
The time is approximately 1767 yr
Example 5 The population of a town increased Trom
37,526 in 1911 to 61,473 in 1931, Find the yearly growth factor assuming it to be constant. If the growth factor has been constant, what was the population in 1901 ine growth factor is given by the following relationships
61,473 -37,52601. + R)
,526
473 7:526
20. Tog ti
16g(1
•
R) 0.0107
1 R1,025
The growth factor 18 1.DL.
The population in 1901 with the same growth fact
given by
37526
Example
(1.025)
29, 300
man earne $2500 a year and invest nac year 18% of it at 56 simple interest. How much interest does he receive in th first three years from the time he bega to invest money in this way?
the man sarna $2500 a year
In each year, he investe 18% of $2500 $450
Investment in the 1st year is $450
Intdrast of lat year 18 5% of $450 -$224
11) Investment in the 3rd year 18 900+ 450
$1,350
Interest of 3rd year 18 5% of $1350 - $672 Hence total interest in the first three years 18, (22
45+ 672) :$135
Solutions for Exercise 5
Suppose that my original capital 18 $100
The of my capital becomes (1 + 3%) of (yor $100)
$34
capital becomes (1
of (por$100)
1770英文中學會考試題預習專欄
堅道英文書院主編 英文科
ENGLISH LANGUAGE (7)
Answer to Exercise 6
Ртес18
(七)
to
To ask for advice, we must know how to separate the sound but impractical one from those which are. helpful. In fact, to ask for advice when one needs. help is unwise. In case we do want advice, we had better consult honestly with those who are of different character, circumstances and thought so that we may see all sides. of the question. But, never ask for advice again after one has made up one's mand to act for those whom have been consulted with will be annoyed to find their advice, after all, to be neglected, as to offering advice, it is unwise Suggest in the direct way especially at the wrong moment or with an endless talk. It is desirable to make clear he's motive and be practicable when one offers advice. To feel with your friend whom you are going to suggest is important. Going back upon the past should be discouraged unless it may lead to some: saeful conclusion. Before we give suggestion to i man who differs much from our point of view," wa haoj better tell ầm this frankly and put our own principles before him to let him decide for himself,
Comprehension
believe that life involves suffering
their teachings include a constructive Bide
one's desires
4. None of them a right, che correct answer 45 TAL
"personal-conduct than to external cites and ceremonies and knowledge")
d, one's ethical and moral nenaviour.
the
were. uedless
7. d. no God creates the worio
8. a, to be a saint is.
Exercise:
better,
than to be a God
Choose the correct answer to sach of the followinga
I was used to
was in Canton.
a. Visit by visiting.
d. make a visit
owupy Sunday when I
pay a vi
"What did you see when you were standing by the window?"
"Well saw John
crossed
b. crossing.
had crossed
read
стова
has
P(1+
Hence 800
'And
P(1
800
(-1.04)
773928
The sum of money is $739.8
Examples
A man borrows, £5000 at 35 p.a. compounc interest, compounded yearly, and repaye £300 at the end of each year. Find the amount of the loan outstanding at the beginning of the 4th year.
5000(1 + 0.03) Amount at the end of Ist year =
5150 Principal at the beginning of 2nd year - 5150.
• £4850. Amount at the end of 2nd year i 4850(1+0.03)
£4995.5.
Principal at the beginning of 3rd year 4795.5 - 300. Amount at the end of 3rd year - 4695.5(1+0.03
- £4836.365
of my capital becomes
the total sum of
6%) of
of $100)
f capital ($100) becomes 1 $103
i.e. my capital increases by 33 Hence
the ♬ increase on the whole • $100
Let his original income be $100
His original saving will be $20
His original expenditure will then be 380
his expenditure be increased by 35%
80 x
$28
100
His expenditure will now be $108
With 10% saving; his come 11 64 108
$120
300
dia income must be increased by 20%
·Let $100 ba the cost of production The Catalogue price will be $180
£4695.1
Salling price of the manufacturer 180 x
$108
100
Percentage profit made by the manuf
Selling price of the ¤18)
300
..108)
Gain % of the distributor
75=8135
100
108
Francapal at the bel
of 4th year
4836.365
What are you looking at?" You've been standing. there for several minutes.
"I see Johns with a man in the corner of the street
argued b.rguing
nad sangued
The man appeared finally aftertue
minutes.
awaited
d. had been
o. had been waited
e. should wait waiting
Murne prec9 01 WOTK seems
to be done.
a, nas argued
for some
were waiting.
with great care)
b. to have done
to have been doing to have been done
d. to be doing]
"Would you have gone to their party 15 you)
av had invited b, had not invited
c. had not been invited a were not vited!
were not to be invited
By next June,
wall learn
singing for five year8,
b. is going to lear
will be learning d, will have learned;
will have been learning.
lost one of his urNS,
b, an C. the d. no articat 29 to be used
Yesterday" พลู saw
one-eyed men who had also
He was so nara working, that he rose at sunrise every morning.
a. a ban. c. the d. no artical is to be used
He and his family will leave Hong Kong for British Isles.
a. ab. an c. the d, no artical is to be used
11. Tine makes
worat enemies. friends:
• £4536.365
The amount of the loan outstanding at the beginning of the 4th year is £4536.365 or £4536 78. 40.
Example
The value or a machine depreciates eac year by 10% of its value at the beginn of that year. Its value when new is £ find its value when it is 8 yr. old.
annual multiplying factor 18 1 – 0.1°
The value after 8 yeara = 750(0.9)
Example
£323
In what time will a sum of money double itself at 4% p.a. compound interest?
The annual multiplying factor is 1.04
Percentage profit made by the distributor 25
12.
Wt. of bronze - 20 lb.
it. of copper in the bronze = 20 x
Wt, of tin in the bronze
WEOI Copper To be added to obtain pronze containing 10% of tin by weight
100
17
b. an
the d. no ertical is to be
honesty is the best policy.
a. ab an c. the d. no artical is needed
He was so silly that he attempt was
failure.
a. freedom···
toreguing c. IOTAKNOWN
d. foredoomed e. foreseen
14. The poor man is so subservient to his boss that
what he says.
he has tö
a. endorse
e:
endear
b. endow c. endue 4.
15. He would be imprisoned for being
Loould not pay his debts before Sunday
(未完棒入第六張第三页)
endeavour
if he