WISKUNDE
GRAAD 10
NOG OEFENINGE
Rente, saamgestelde groei, appresiasie, depresiasie, inflasie.
MATHEMATICS
GRADE 10
MORE EXERCISES
Interest, compound growth, appreciation, depreciation, inflation.
Maak gebruik van die formules van enkelvoudige
rente en bereken dan die waarde van elke letter
in die tabel :
Use the formulae to calculate simple interest and
then calculate the value of each letter in the table :
|
|
|
P |
r% |
t (jaar/years) |
I |
A |
Ant. / Ans |
|
1.1 |
|
1.2 |
|
1.3 |
|
1.4 |
245 400 |
18,0 |
1,25 |
g |
h |
A 1.4 |
|
1.5 |
m |
n |
3 |
279,00 |
2 497,00 |
A 1.5 |
|
1.6 |
p |
q |
4 |
3 511,20 |
18 911,20 |
A 1.6 |
|
1.7 |
r |
s |
6 |
211 854,80 |
38 554,80 |
A 1.7 |
|
1.8 |
t |
u |
2,5 |
22 960,00 |
134 960,00 |
A 1.8 |
|
1.9 |
v |
12,2 |
x |
23 365,44 |
68 965,44 |
A 1.9 |
|
1.10 |
y |
6,5 |
z |
9 035,00 |
64 635,00 |
A 1.10 |
|
1.11 |
aa |
8,0 |
bb |
36 048,00 |
148 698,00 |
A 1.11 |
|
1.12 |
cc |
11,2 |
dd |
91 309,40 |
342 159,40 |
A 1.12 |
|
1.13 |
18 650 |
15,24 |
ee |
ff |
25 755,65 |
A 1.13 |
|
1.14 |
35 800 |
22,4 |
gg |
hh |
59 857,60 |
A 1.14 |
|
1.15 |
65 900 |
7,5 |
mm |
nn |
107 911,30 |
A 1.15 |
|
1.16 |
521 000 |
5,4 |
pp |
qq |
619 469 |
A 1.16 |
|
|
|
Maak gebruik van die formules van saamgestelde
rente en bereken dan die waarde van elke letter in
die tabel :
Use the formulae to calculate compound interest
and then calculate the value of each letter in
the table :
|
|
|
P |
r% |
Wanneer |
Tyd |
Aantal |
A |
Ant. / Ans. |
|
|
saamgestel |
(jaar) |
periodes |
|
|
P |
r% |
When |
Time |
Number |
A |
Ant. / Ans. |
|
|
compounded |
(years) |
of periods |
|
|
|
2.1 |
12 500 |
7,8 |
jaarliks / annually |
5 |
a |
b |
A 2.1 |
|
2.2 |
113 600 |
6,5 |
half-jaarliks / semi-yearly |
2,5 |
c |
d |
A 2.2
|
|
2.3 |
250 600 |
8,2 |
kwartaalliks / quarterly |
3 |
e |
f |
A 2.3
|
|
2.4 |
85 600 |
6,4 |
maandeliks / monthly |
2,5 |
g |
h |
A 2.4
|
|
2.5 |
m |
7,2 |
maandeliks / monthly |
n |
36 |
80 371,54 |
A 2.5
|
|
2.6 |
p |
8,8 |
kwartaalliks / quarterly |
q |
16 |
261 201,25 |
A 2.6
|
|
2.7 |
r |
9,5 |
half-jaarliks / semi-yearly |
5,5 |
s |
201 594,98 |
A 2.7
|
|
2.8 |
t |
11,5 |
jaarliks / annually |
2,5 |
u |
216 769,99 |
A 2.8
|
|
2.9 |
350 000 |
w |
maandeliks / monthly |
x |
36 |
464 894,71 |
A 2.9
|
|
2.10 |
230 600 |
y |
maandeliks / monthly |
z |
60 |
335 129,69 |
A 2.10
|
|
2.11 |
240 000 |
aa |
kwartaalliks / quarterly |
3 |
bb |
306 173,32 |
A 2.11
|
|
2.12 |
450 600 |
cc |
kwartaalliks / quarterly |
2,5 |
dd |
608 514,80 |
A 2.12
|
|
2.13 |
180 750 |
ee |
half-jaarliks / semi-yearly |
ff |
6 |
226 080,15 |
A 2.13
|
|
|
|
Maria wil R20 000 vir 3 jaar belê. Sy word twee
moontlikhede aangebied. Help haar asseblief
om die beste keuse te maak.
Moontlikheid 1: Belê die geld teen 7,5% per jaar
en die rente word half-jaarliks
saamgestel.
Moontlikheid 2: Belê die geld teen 8% per jaar
en die rente word jaarliks
saamgestel.
Maria wants to invest R20 000 for 3 years. She is
offered two possibilities. Please help her to make
the best decision.
Possibility 1 : Invest the capital at 7,5% per annum
and the interest is accrued
semi-annually.
Possibility 2 : Invest the capital at 8% per annum
and the interest is calculated
semi-annually.
4. Die waarde van 'n vragmotor is tans R885 000.
Bereken die waarde daarvan oor 5 jaar as die
depresiasie teen 7,5% per jaar bereken word.
Ant. 4
4. The present value of a lorry is R885 000.
Calculate its value 5 years from now if the
depreciation is calculated at 7,5% p.a.
Ans. 4
5. Die waarde van 'n masjien is R275 650. Bereken
die waarde van die masjien na 5 jaar as die
masjien teen 12% per jaar gedepresieer word.
gedepresieer word.
Ant. 5
5. The value of a machine is R275 650. Calculate the
value of the machine after 5 years if the machine
is depreciated at 12% per annum.
Ans. 5
6. Die aantal inwoners van 'n stad is tans 3 105 560.
Bereken die aantal inwoners oor 4 jaar as die
bevolkingstoename 6,% per jaar is.
Ant. 6
6. The number of inhabitants of a city is 3 105 560
at present. Calculate the number of inhabitants
4 years later if the increase in popoulation is
6,5% per annum.
Ans. 6
7. 'n Masjien kos nou R45 800. Wat sal die
masjien oor 4 jaar kos as die inflasiekoers
6,8% per jaar is?
Ant. 7
7. Presently the price of a machine is R45 800. What
will the price be 4 years from now if the rate of
inflation is 6,% p.a.?
Ans. 7
8. Jan wil 'n sekere soort masjien koop. Die koste
van die masjien is tans R48 350. Jan het nie
nou die geld nie. Hy belê R33 000 teen 8,2%
per jaar maandeliks saamgestel. Die koste van
die masjien styg a.g.v. inflasie. Die inflasiekoers
is 5,8% per jaar. Sal Jan oor 3 jaar genoeg
geld hê om die masjien te kan koop?
Ant. 8
8. John wants to buy a certain type of machine.
At the moment the machine costs R48 350.
costs R48 350. John does not have sufficient
funds. He invests R33 000 at 8,2% per annum
compoundedd monthly. Due to inflation the price
of the machine increases at 5,8% p.a. Will John
have sufficient funds at the end of 3 years?
Ans. 8
9. Pieter het R1 200 in 'n spaarrekening waarop
hy 7,5% enkelvoudige rente verdien. Hy wil 'n
DVD-speler, wat teen R1 150 kontant
geadverteer word, koop. Die speler kan ook
op huurkoop gekoop word. Daar is 'n 10%
deposito en 24 maandelikse paaiemente
van R55,00 van toepssing.
9.1 Hoeveel geld het hy in sy spaarrekening aan
die einde van 3 jaar?
9.2 Hoeveel betaal hy vir die speler as hy dit
op huurkoop, koop?
9.3 Die gemiddelde inflasiekoers is 6,85% p.a.
Wat sal die speler oor 3 jaar kos?
Ant. 9
9. Peter has R1 200 in a savingsaccount on
on which he receives 7,5% simple interest.
He wants to buy a DVD player that is advertised
at R1 150 as a cash sale. The player is also sold
on hire-purchase. A 10% deposit and 24 monthly
instalments of R55,00 are required.
9.1 What will the balance in his savings account
be at the end of 3 years?
9.2 What does he pay for the player on hire-purchase?
9.3 The average rate of inflation is 6,85% p.a. What will
the cost of the player be after 3 years?
Ans. 9
10. 'n Bedrag van R6 700 word belê en die rente
word halfjaarliks saamgestel. Na 4 jaar is daar
R10 380,27 in die rekening. Bereken die
jaarlikse rentekoers, korrek tot 2 desimale syfers.
Ant. 10
10. An amount of R6 700 is invested and the interest
is compounded half-yearly. After 4 years the
balance in the account is R10 380,27. Calculate
the interest rate per annum, correct to
2 decimal places.
Ans. 10
11. Normaalweg kos 'n TV-stel R4 500. Dit kan op
huurkoop onder die volgende voorwaardes
gekoop word : 'n Deposito van R675,
12,5% rente op die uitstaande bedrag en
24 maandelikse paaiemente.
11.1 Bereken die persentasie van die deposito.
11.2 Bereken die bedrag van die maandelikse
paaiement.
11.3 Bereken die ekstra koste om die TV-stel
op huurkoop te koop.
Ant. 11
11. Usually a TV set costs R4 500. It can be bought
on hirepurchase on the following conditions :
A deposit of R675, an interest rate of
12,5% and 24 monthly instalmants.
11.1 Calculate the percentage of the deposit to
be paid.
11.2 Calculate the monthly instalmant.
11.3 Calculate the exta cost to buy he TV set on
hire-purchase.
Ans. 11
12. Anna wil 'n yskas koop. Die kontantprys is
R2 490. Die yskas kan ook op huurkoop
gekoop word. Die deposito is 10% van
die koopprys en die uitstaande bedrag
moet met 30 maandelikse paaiemente
van R137,00 betaal word.
12.1 Bereken die deposito gevra.
12.2 Bereken die enkelvoudige rentekoers wat op
die uitstaande bedrag gehef word.
12.3 Bereken die ekstra koste.
12.4 Anna wil kontant betaal. Watter bedrag moet
sy vir 30 maande teen 8,25% per jaar belê
en die rente word maandeliks saamgestel?
Ant. 12
12. Ann wants to buy a fridge. The cash price is
R2 490. The fridge can also be bought on
hire-purchase. The deposit is 10% of the
costprice and the balancemust be paid by
30 monthly instalments of R137,00.
12.1 Calculate the deposit that has to be paid.
12.2 Calculate the simple interest rate that has
to be paid on the outstanding amount.
12.3 Calculate the extra cost.
12.4 Ann wants to pay cash. What amount must
she invest for 30 months at an interest rate
of 8,25% p.a. and the interest is
compounded monthly?
Ans. 12
13. Petrus wil 'n sitkamerstel koop. Die kontantprys
is R15 000. Hy wil kontant vir die stel betaal
maar hy het nie genoeg geld nie. Hy aanvaar
dat die prys van die stel met 7,25% per jaar
weens inflasie sal styg. Hy besluit om genoeg
geld te belê sodat hy die stel oor 3 jaar kan koop.
Die rentekoers op sy beleging is 5,4% per jaar
maandeliks saamgestel.
13.1 Wat sal die stel oor 3 jaar kos?
13.2 Watter bedrag moet Petrus nou belê om
oor 3 jaar kontant vir die stel te kan betaal?
Ant. 13
13. Peter wants to buy a lounge suite. The cash
price is R15 000. He wants to pay cash but
does not have enough money. He accepts that the
price of the suite will increase at a rate of
7,25% p.a. due to inflation. He decides to invest
enough money so that he can pay cash for the
suite after 3 years. The interest rate on his
investment is 5,4% p.a., monthly compounded.
13.1 What will the cost of the suite be 3 years from
now?
13.2 What amount must Peter invest now in order to
pay cash for the suite 3 years later?
Ans. 13
14. Sarie wil 'n sitkamerstel koop. Die kontantprys
is R6 999. Op huurkoopooreenkoms word 'n
deposito van R770 vereis. Die balans moet
oor 30 maande betaal word en die
enkelvoudige rentekoers is 12% per jaar.
Daar word ook 'n maandelikse bedrag van
R20 gehef vir versekering. Bereken die
14.1 maandelikse paaiement.
14.2 totale bedrag wat Sarie vir die stel betaal.
14.3 ekstra koste om die stel op huurkoop
te koop.
Ant. 14
14. Sarah wants to buy a lounge suite. The cash price
is R6 999. On hirepurchase a deposit of R700 is
necessary. The balance must be paid over a
period of 30 months and the simple interest rate
is 12% p.a. Also a monthly amount of R20 is
added for the insurance premium.
Calculate the
14.1 monthly instalment.
14.2 total amount that Sarah pays for the set.
14.3 extra cost to buy the set on hire-purchase.
Ans. 14
15. Thabo belê R10 350 teen 6,5% p.j., jaarliks
saamgestel vir 4 jaar. Na 4 jaar word die
rentekoers verhoog na 7,2% per jaar, jaarliks
saamgestel. Vyf jaar na die eerste belegging
onttrek Thabo R6 300. Hoeveel geld is daar
in die rekening na 8 jaar?
Ant. 15
15. Thabo invests R10 350 at 6,5% p.a., yearly
compounded for 4 years. After 4 years the
interest rate is increased to 7,2% p.a,, yearly
compounded. Five years after the initial
investment Thabo withdraws R6 300. What
is the balance of the account after 8 years?
Ans. 15
16. Pieter belê R13 400 teen 6,2% p.a., jaarliks
saamgestel vir 2 jaar. Hy belê 'n verdere
R3 800 2 jaar na sy eerste belegging.
Na 3 jaar word die rentekoers verlaag na
5,8% p.a., jaarliks saamgestel. 5 jaar na
die aanvanklike belegging, belê Pieter
'n verdere R2 500. Wat bedra die saldo
in die rekening na 7 jaar?
Ant. 16
16. Peter invests R13 400 at 6,2% p.a.,
compounded yearly for 2 years. He invests
an additional R3 800 2 years after his initial
investment. After 3 years the interest rate
is lowered to 5,8% p.a., compounded
yearly. 5 years after the initial investment
Peter invests another R2 500. What is the
total amount in the account after 7 years?
Ans. 16
17. Sandri belê R7 300 teen 7,8% per jaar
halfjaarliks saamgestel vir 30 maande. Die
rentekoers word nou verlaag na 6,6% per jaar,
maandeliks saamgestel. 3 jaar na die eerste
belegging onttrek Sandri R4 800. Watter
bedrag is daar in die rekening na 4 jaar?
Ant. 17
17. Sandy invests R7 300 at 7,8% p.a. compounded
semi-annually for 30 months. The interest rate is
now reduced to 6,6% per year, compounded
monthly. 3 years after the first investment Sandy
withdraws R4 800. What balance is there in the
account after 4 years?
Ans. 17