Question $2$

$2\mathrm{.}1$ Anisha and Lindiwe each received R$12000$ to invest for a period of $5$ years. They invested

the money at the same time according to the following options :

$$ Anisha : $8\mathrm{.}5\%$ p$.$a$.$ simple interest. At the end of $5$ years she will receive an additional

bonus pay$-$out of exactly $7\mathrm{.}5\%$ of the original amount invested.

$$ Lindiwe : $8\mathrm{.}5\%$ compounded quartelyWho will have the larger final amount after $5$ years? Justify your answer with appropriate

calculations. $[6]$

$2\mathrm{.}2$ Tebogo opened a savings account with a single deposit of R$5000$ at the begining of June

$2015.$ He then made $24$ monthly deposits of R$800$ at the end of every month, starting at the

end of June $2015.$ The account earned interest at $15\%$ p$.$a$.$ compounded monthly.

Calculate the amount that should be in his savings account immediately after he makes the

last deposit. $[5]$

$2\mathrm{.}3$ At what annual percentage interest rate, compounded quartely, should a lump sum be

invested in order for it to double in $6$ years? $[5]$

Question $3$

$3\mathrm{.}1$ Suppose you want to R$30000$ in the bank and at the begining of each year you deposit R$969$

at an interest rate of $4\%.$ For how long will it take you to have R$30000$ in the bank? $[6]$

$3\mathrm{.}2$ John wants to apply for a loan, payable over a period of $5$ years from a bank that charges

$12\%$ interest p$.$a$.,$ compounded annually. If he can on;y be able to pay back R$10000$ p$.$a$.$ at

the begining of each year, What is the loan amount he will get?