WISKUNDE
GRAAD 10
NOG OEFENINGE
  
Rente, saamgestelde groei, appresiasie, depresiasie, inflasie.
  
MATHEMATICS
GRADE 10
MORE EXERCISES
  
Interest, compound growth, appreciation, depreciation, inflation.
  
Vraag / Question  1

            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
    4 500 6,5     4     a     b     A 1.1
1.2
  18 800 8,2     2,5     c     d     A 1.2
1.3
  12 250 12,5    12     e     f     A 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
     

Vraag / Question  2

            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
  
                    

Vraag / Question  3

          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.
  
Antwoord / Answer  3


  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
  
  
  
  
  
  
  
  
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