Question $3\mathrm{.}1($Time Value of Money$)$

$3\mathrm{.}1\mathrm{.}1$ Standard Bank has offered Tsholofelo an investment account which requires a

minimum investment of R$100000.$ The account offers an interest rate of $30\%$ per year,

interest compounded semi $-$ annually $.$

What is the annual effective interest rate?

Use the following formula. Round off to $2$ decimal places $.$

$[r_e=(1+\frac{r}{m}{)}^m-1]100$

$3\mathrm{.}2\mathrm{.}1$ Tsebo Utlwa has decided that she need to invest R$1000000$ in savings at rate

of $30\%$ per annum compounded annually for a period $10$ years. How much is the end

value of this investment.

$3\mathrm{.}3\mathrm{.}1$ Suppose that Tsebo Utlwa decides to invest the same amount of R$1000000$ for

$30\%$ per annum with compounded quarterly for a period of $10$ years. How much

will have accumulated at the end of $10$ years.

$3\mathrm{.}4\mathrm{.}1$ Ashlei based in Durban expects to receive R$900000$ in $5$ years' time now from

his father as part of her profit sharing from their business they operate in Durban. The

current rate of interest is $20\%$ per annum compounded annually.

Required.

Calculate the Present Value on the amount expected to be received by Ashlei $.$