MATHEMATICS

GRADE $10$

$2$

SEPTEMBER $2024$

QUESTION $1$

$1\mathrm{.}1.$ Seven years ago, Mrs Hlongwane decided to invest R$18000$ in a bank account that paid simple interest at $4,5\%$ p$.$a

$1\mathrm{.}1\mathrm{.}1.$ Calculate how much interest Mrs Hlongwane has earned over the $7$ years.

$1\mathrm{.}1\mathrm{.}2.$ Mrs Hlongwane wants to buy a television set that costs R$27660,00$ now. If the average rate of inflation over the last $5$ years was $6,7\%$ p$.$a$.$ calculate the cost of the television set $5$ years ago.

$(3)$

$1\mathrm{.}1\mathrm{.}3.$ At what rate of simple interest should Mrs Hlongwane have invested her money $7$ years ago if she intends buying the television set now using only her original investment of R$18000$ and the interest earned over the last $7$ years.

$1\mathrm{.}2.$ A sum of money doubles in $5$ years when the interest is compounded annually. Calculate the rate of interest.

QUESTION $2$

$[11]$

$2\mathrm{.}1.$ Thando has R$4500$ in his savings account. The bank pays him a compound interest rate of $4,25\%$

p$.$a$.$ Calculate the amount Thando will receive if he decided to withdraw the money in $3$ years. the balance by means of hire$-$purchase agreement. The rate of interest on the loan is $16,25\%$ p$.$a$.$ simple interest. The repayment period of the loan is $54$ months. In addition to the hire$-$purchase agreement, an annual insurance premium of $1,5\%$ of the total cost of the fridge should be added. The annual insurance premium should be paid monthly

$2\mathrm{.}2\mathrm{.}1.$ Calculate the value of the loan that Mary will take.

$2\mathrm{.}2\mathrm{.}2.$ Calculate the total amount that must be repaid on the hire$-$purchase agreement. $=?$

$2\mathrm{.}2\mathrm{.}3.$ Calculate the monthly repayments, which includes the monthly insurance premium

$[11]$