Gebruik die formules vir enkelvoudige rente om die
waarde van elke letter in die tabel te bereken :
Use the formulae for
simple interest to calculate
the value of each letter :
| Nommer |
Kapitaal, R |
Rentekoers, % |
Tydperk, jaar |
Bedrag, R |
Rente, R |
Antwoorde |
| Number |
Capital, R |
Interest rate, % |
Time, years |
Amount, R |
Interest, R |
Answers |
| 1.1 |
1 200 |
5 |
2 |
a |
b |
A 1.1 |
| 1.2 |
22 500 |
7 |
4 |
c |
d |
A 1.2 |
| 1.3 |
23 650 |
9 |
3,5 |
e |
f |
A 1.3 |
| 1.4 |
80 000 |
12 |
8 |
g |
h |
A 1.4 |
| 1.5 |
m |
18 |
1,5 |
149 860 |
n |
A 1.5 |
| 1.6 |
p |
25 |
0,5 |
737 820 |
q |
A 1.6 |
| 1.7 |
r |
4 |
4 |
2 668 |
s |
A 1.7 |
| 1.8 |
t |
5,2 |
3 |
18 496 |
v |
A 1.8 |
| 1.9 |
28 650 |
w |
5,5 |
50 710,50 |
x |
A 1.9 |
| 1.10 |
108 000 |
y |
8 |
182 304 |
z |
A 1.9 |
| 1.11 |
530 000 |
aa |
15 |
1 484 000 |
bb |
A 1.11 |
| 1.12 |
850 800 |
cc |
13 |
2 012 142 |
dd |
A 1.12 |
| 1.13 |
850 |
11,4 |
ee |
1 189,15 |
ff |
A 1.13 |
| 1.14 |
6 820 |
8,8 |
gg |
8 170,36 |
hh |
A 1.14 |
| 1.15 |
9 730 |
6,4 |
mm |
nn |
3 736,32 |
A 1.15 |
| 1.16 |
12 500 |
5,8 |
pp |
qq |
6 343,75 |
A 1.16 |
Gebruik die formules vir saamgestelde rente en bereken dan
die waarde van elke letter in die tabel :
Use the formulae for compound interest and then calculate
the value of each letter in the table :
| Nommer |
Kapitaal, R |
Rentekoers, % |
Tydperk, jaar |
Wanneer saamgestel |
Aantal periodes |
Bedrag, R |
Antwoorde |
| Number |
Capital, R |
Interest rate, % |
Time, years |
When compounded |
Periods, number |
Amount, R |
Answers |
| 2.1 |
250 |
6 |
1 |
jaarliks / annually |
a |
b |
A 2.1 |
| 2.2 |
1 200 |
10 |
1 |
half-jaarliks / semi-annually |
c |
d |
A 2.2 |
| 2.3 |
13 450 |
8 |
5 |
kwartaalliks / quarterly |
e |
f |
A 2.3 |
| 2.4 |
21 560 |
9,4 |
g |
maandeliks / monthly |
18 |
h |
A 2.4 |
| 2.5 |
124 500 |
12 |
m |
maandeliks / monthly |
36 |
n |
A 2.5 |
| 2.6 |
p |
8,8 |
q |
kwartaalliks / quarterly |
16 |
261 201,25 |
A 2.6 |
| 2.7 |
r |
9,5 |
5,5 |
half-jaarliks / semi-annually |
s |
201 594,98 |
A 2.7 |
| 2.8 |
t |
11,5 |
2,5 |
jaarliks / annually |
u |
216 769,99 |
A 2.8 |
| 2.9 |
v |
8,4 |
w |
half-jaarliks / semi-annually |
5 |
10 465,94 |
A 2.9 |
| 2.10 |
6 400 |
x |
8 |
kwartaalliks / quarterly |
y |
9 829,70 |
A 2.10 |
| 2.11 |
240 000 |
aa |
3 |
kwartaalliks / quarterly |
bb |
306 173,32 |
A 2.11 |
| 2.12 |
450 600 |
cc |
2,5 |
kwartaalliks / quarterly |
dd |
608 514,80 |
A 2.12 |
| 2.13 |
180 750 |
ee |
ff |
half-jaarliks / semi-annually |
6 |
226 080,15 |
A 2.13 |
R6 700 word belê en 4 jaar later is
die balans in die rekening R10 380,27.
Rente word half-jaarliks saamgestel. Bereken
die jaarlikse rentekoers, korrek tot twee
desimale syfers.
[ 3 ]
R6 700 is invested and 4 years later the
balance in the account is R10 380,27.
Interest is compounded semi-annually.
Calculate the annual rate of interest,
correct to two decimal digits.
[ 3 ]
‘n Masjien kos nou R116 850. Wat sal die
masjien oor 5 jaar kos as die inflasie
koers 7,4% p.j. is?
[ 4 ]
A certain piece of machinery now costs
R116 850. What will the machine cost
in 5 years time if the rate of inflation
is 7,4% p.a.?
[ 4 ]
Die prys van ’n DVD speler is R1 245.
Wat sal die speler oor 3 jaar kos as die
inflasie koers 5,2% p.j. is?
[ 5 ]
The price of a DVD player is R1 245.
What will the player cost 3 years later if the
rate of inflation is 5,2% p.a.?
[ 5 ]
Op die oomblik bestaan ’n kolonie pikkewyne
uit 650 voëls. Uit hoeveel voëls sal die kolonie
oor 3 jaar bestaan as die aanwaskoers
2,1% p.j. is?
[ 6 ]
At present a colony of penguins consists
of 650 birds. If the rate of increase
is 2,1%, how many birds will there be in
3 years time?
[ 6 ]
Die waarde van ’n motor is R120 000.
Wat sal die waarde van die motor oor 5 jaar
wees as die depresiasiekoers 15% p.j. is en
reguitlyn depresiasie word gebruik?
[ 7 ]
The value of a motor car is R120 000.
What will its value be in 5 years time if
the rate of depreciation is 15% p.a. and
straight line depreciation is used?
[ 7 ]
Reguitlyn depresiasie word gebruik om die
waarde van ’n trekker oor 4 jaar te bereken
as depresiasie teen ’n koers van 12% p.a.
toegepas word en die huidige waarde van
die trekker is R450 000.
[ 8 ]
Straight line depreciation is used to
determine the value of a tractor 4 years
from now if the rate of depreciation is
12% p.a. and the present value of the
tractor is R450 000.
[ 8 ]
’n Masjien se waarde is R84 500. Wat sal
die waarde van die masjien oor 3 jaar wees
as die waarde teen 18% p.j. verminder word
deur verminderde balans depresiasie te gebruik?
[ 9 ]
A machine has a value of R84 500. What
will the value of the machine be 3 years
from now if value is decreased at 18% p.a.
using the reducing-balance method?
[ 9 ]
’n Firma koop ’n masjien wat R215 700 kos.
Die waarde van die masjien word teen
11,2% p.a. depresieer deur middel van die
verminderde balans metode. Bereken die
waarde van die masjien aan die einde van 5 jaar.
[ 10 ]
A business buys a machine that costs
R215 700. The value of the machine
depreciates at 11,2% p.a. using the
diminishing-balance method.
Determine the value of the machine at
the end of 5 years.
[ 10 ]
’n Maatskappy koop ’n vragmotor teen
R530 650. Die waarde van die
vragmotor word teen 8% p.j. verminder
volgens die verminderde balans metode.
11.1 Bereken die waarde van die vragmotor
aan die einde van 5 jaar.
[ 11.1 ]
11.2 Bepaal die waarde van ’n nuwe vragmotor
oor 5 jaar as die inflasiekoers 7% p.j. is.
[ 11.2 ]
11.3 Bereken die bedrag wat die maatskappy
nou moet belê om ’n nuwe vragmotor oor
5 jaar te kan koop as die rentekoers
konstant teen 7,2% p.j. kwartaalliks
saamgestel, bly.
[ 11.3 ]
A business buys a lorry that costs
R530 650. The value of the lorry
depreciates at 8% p.a. using the
diminishing-balance method.
11.1 Determine the value of the lorry at
the end of 5 years.
[ 11.1 ]
11.2 Determine the value of a new lorry at
the end of 5 years if the rate of
inflation is 7% p.a.
[ 11.2 ]
11.3 Determine the amount that the business
must now invest to buy a new lorry at
the end of the 5 years if the rate of
interest remains constant at 7,2% p.a.
compounded quarterly?
[ 11.3 ]
Die waarde van ’n masjien word teen 12%
per jaar volgens die verminderde balans
metode verminder. Na hoeveel jaar sal
die waarde van die masjien ’n kwart van
sy oorspronklike koopprys hê?
[ 12 ]
The value of a machine is diminished at
12% per annum according to the
diminishing-balance method.
After how many years will the value of
the machine be a quarter of its original
cost price?
[ 12 ]
Die waarde van ’n masjien word depresieer
teen ’n koers van 12% per annum met die
verminderde balans metode. Na hoeveel jaar
sal die waarde van die masjien met ’n derde
van sy oorspronklike prys verminder?
[ 13 ]
The value of a machine depreciates at
12% per annum according to the
diminishing-balance method. After how
many years will the value of the machine
be diminished by a third of its original
cost price?
[ 13 ]
Jasper belê R40 000 vir 5 jaar.
Gedurende die eerste twee jaar is die
rentekoers konstant teen 18% p.j. maandeliks
saamgestel. Die koers word nou verander
na 12% p.j. kwartaalliks saamgestel.
Bereken die waarde van die belegging aan
die einde van 5 jaar.
[ 14 ]
Jasper invests R40 000 for 5 years.
During the first two years the interest rate
is 18% p.a. compounded monthly.
The rate of interest is now increased to
12% p.a. compounded quarterly.
Calculate the value of the investment at
the end of 5 years.
[ 14 ]
Jakobus belê ’n sekere bedrag vir 3 jaar.
Gedurende die eerste jaar is die rentekoers
8% per jaar, kwartaalliks saamgestel en vir
die laaste twee jaar is die koers 10% per jaar,
half-jaarliks saamgestel. Aan die einde van
die 3 jaar is die waarde van die belegging
R23 682,66. Bepaal die bedrag wat
oorspronklik belê is.
[ 15 ]
James invests a certain amount for 3 years.
During the first year the rate of interest is
8% per annum, quarterly compounded and
for the last two years the rate is 10% per
year, compounded semi-annually.
At the end of the 3 years the value of the
investment is R23 682,66. Determine the
amount originally invested.
[ 15 ]
Johannes belê R30 000 vir 5 jaar.
Die rentekoers is 18% p.j., maandeliks
saamgestel. Na 2 jaar onttrek hy R8 000
en 1 jaar later onttrek hy ’n verdere R6 000.
Wat is die waarde van die belegging aan
die einde van die 5 jaar?
[ 16 ]
John invests R30 000 for 5 years.
The interest rate is 18% p.a., compounded
monthly. After 2 years he withdraws
R8 000 and 1 year later he withdraws a
further R6 000. What is the value of the
investment at the end of the 5 years?
[ 16 ]
Marie belê R130 000 vir 2 jaar teen ’n
rentekoers van 6% per annum, maandeliks
saamgestel. Na 4 maande onttrek sy
R20 000 en 7 maande later ’n verdere
R15 000. Wat is die waarde van die
belegging aan die einde van die
2 jaar periode?
[ 17 ]
Mary invests R130 000 for 2 years at an
interest rate of 6% per annum,
compounded monthly. After 4 months she
withdraws R20 000 and 7 months later
another amount of R15 000. What is the
value of the investment at the end of
the 2 year period?
[ 17 ]
’n Bedrag van R82 000 word vir 3 jaar teen
’n konstante rentekoers van 8% p.j.
half-jaarliks saamgestel, belê. Na 6 maande
word nog R8 000 belê en 1 jaar later nog
R12 000. Bepaal die waarde van die
belegging aan die einde van die
3 jaar periode.
[ 18 ]
An amount of R82 000 is invested for
3 years at a constant rate of interest of
8% p.a. compounded semi-annually.
After 6 months a further R8 000 is
invested and 1 year later another
R12 000 is invested. Determine the
value of the investmen at the end of
the 3 year period.
[ 18 ]
Johannes belê R65 000 vir 2 jaar teen
’n rentekoers van 8% kwartaalliks saamgestel.
Na 4 maande belê hy nog R5 000. Een jaar
later onttrek hy R12 000. Hoeveel geld is
daar aan die einde van die 2 jaar periode in
die rekening?
[ 19 ]
John invests R65 000 for 2 years at an
interest rate of 8% compounded quarterly.
After 4 months he invests a further R5 000.
One year later he withdraws R12 000.
How much money is there in the account
at the end of the 2 year period?
[ 19 ]
Willem belê R55 600 teen ’n rentekoers van
15% p.a., maandeliks saamgestel vir 5 jaar.
Na 1 jaar belê hy nog R12 000.
Een jaar later onttrek hy R20 000 en die
rentekoers verander na 10% p.a.,
kwartaalliks saamgestel. Vier jaar na die
eerste belegging belê Willem ’n verdere
R8 300. Wat is die waarde van die
belegging na 5 jaar?
[ 20 ]
William invests R55 600 at a rate of
interest of 15% p.a., monthly compounded
for 5 years. After 1 year he invests a
further R12 000. One year later he witdraws
R20 000 and the rate of interest is
decreased to 10% p.a., quarterly compounded.
Four years after the initial investment
William invests a further R8 300. What is
the value of the investment after 5 years?
[ 20 ]
R20 000 word belê teen 6% p.j.,
maandeliks saamgestel. Bereken die
effektiewe rentekoers.
[ 21 ]
R20 000 is invested at 6% p.a.,
monthly compounded. Calculate the
effective interest rate.
[ 21 ]
Die effektiewe rentekoers is 2,02%.
Wat is die nominale rentekoers as dit
kwartaalliks saamgestel word?
[ 22 ]
The effective interest rate is 2,02%.
What is the nominal rate of interest
if it is compounded quarterly?
[ 22 ]
R35 500 word belê vir 3 jaar teen
8% p.j., half-jaarliks saamgestel.
23.1 Bereken die waarde van die
belegging na 3 jaar.
[ 23.1 ]
23.2 Bereken die effektiewe rentekoers.
[ 23.2 ]
R35 500 is invested for 3 years at
8% p.a., semi-annually compounded.
23.1 Calculate the value of the investment
after 3 years.
[ 23.1 ]
23.2 Calculate the effective interest rate.
[ 23.2 ]
'n Belegging moet rente verdien teen
6,25 % per jaar, kwartaalliks saamgestel.
Bereken die effektiewe jaarlikse rente
koers op die belegging.
[ 24 ]
An investment must earn interest at a rate
of 6,25 % per annum, compounded
quarterly. Calculate the effective annual
interest rate on this investment.
[ 24 ]
Bereken die effektiewe rentekoers as
rente half-jaarliks saamgestel word
teen 12 % per jaar.
[ 25 ]
Calculate the effective interest rate
if interest is compounded at
12 % per annum, compounded
semi-annually.
[ 25 ]
'n Maatskappy het gereedskap ter
waarde van R160 000 gekoop.
Na 5 jaar is die boekwaarde van die
gereedskap R40 000 as die
verminderde saldo metode gebruik
word. Bereken die depresiasie koers.
[ 26 ]
A company bought machinery costing
R160 000. Using the reducing balance
method, the machinery had a book
value of R40 000 after 5 years.
Calculate the rate of depreciation.
[ 26 ]