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    <pre style="white-space:pre-line"><code>Senior Phase Mathematics: Grade 7 â€“ 9                                                                        Learner book

                       Unit 1.7: Simple and compound interest

Simple interest
Simple interest is interest charged (or earned) on the initial amount borrowed (or invested).

         Worked example:

If I invest R500 in an account that pays 10% simple interest per year, I will earn 10% of                         Grade 7, 8 and 9

R500  =  à¬µà¬´   àµˆ  R500  àµŒ  R50  as  interest  each  year.  So  if  I  invest  it  for  3  years,  Iâ€™ll  earn
         à¬µà¬´à¬´

3 àµˆ R50 àµŒ R150 in interest. So at the end of 3 years, Iâ€™ll have R650 in total.

We use the formula:

A àµŒ Páˆº1 àµ… Ý…ÝŠáˆ»                            A = total paid back (loan) or accumulated (investment)
  SI àµŒ P. ÝŠ. Ý…                           SI = simple interest charged (loan) or earned (investment)
                                         P = amount borrowed (loan) or invested (investment)
                                         Ý… = interest rate
                                         ÝŠ = number of years

Hire Purchase

 Customer wants           â†’      Store allows      â†’         Store charges                       Customer pays
to buy something               customer to pay            simple interest on                   off the loan plus
                                                          loan and calculates            â†’ interest in
  expensive but                  a deposit and                                                 monthly amounts
doesnâ€™t have cash                  remaining                 how much the
                                                            customer owes                                         Grade 8 and 9
   to pay for it               amount is a loan
   immediately

         Worked example:
         I buy a fridge on hire purchase for R3 000. I pay a 10% deposit. The store
         charges 25% interest per year and allows me to pay it back over 2 years.
         How much do I need to repay each month?

         Deposit = 10% of R3 000 = R300

         So hire purchase loan = R3 000 â€“ R300 = R2 700

         Amount I need to repay including interest:

         A àµŒ Páˆº1 àµ… Ý…ÝŠáˆ»                       P àµŒ R2 700; Ý… àµŒ 25% àµŒ 0,25; ÝŠ àµŒ 2

         A àµŒ R2 700áˆº1 àµ… 0,25 àµˆ 2áˆ» àµŒ R4 050

         R4   050  over  24  months  is  à­–à¬¸à¬´à¬¹à¬´  àµŒ  R168,75  per      month.
                                           à¬¶à¬¸

Compound interest

Compound interest is interest charged (or earned) on the initial amount, as well as on any

interest already charged (or earned).

We use the formula:                             A = total paid back (loan) or accumulated (investment)            Grade 9
                                                P = amount borrowed (loan) or invested (investment)
        A àµŒ Páˆº1 àµ… Ý…áˆ»à¯¡                           Ý… = interest rate
                                                ÝŠ = number of years

         Worked example:
         I invest R5 000 in the bank for 6 years and they pay me 8% compound interest
         per year. How much will I have in the bank after 6 years?

         A àµŒ Páˆº1 àµ… Ý…áˆ»à¯¡                       P àµŒ R5 000; Ý… àµŒ 8% àµŒ 0,08; ÝŠ àµŒ 6

         A àµŒ R5 000áˆº1 àµ… 0,08áˆ»à¬º

         àµŒ R5 000áˆº1,08áˆ»à¬º àµŒ R7 934,37

Winning Teams & OLICO                                                                                                               21</code></pre>
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