Question $3$

$[23$ Marks$]$

Refer to the following independent scenarios and answer the questions that follow:

a$)$ On $1$ January $2013.$ you had R$8000,$ which you invested in a fixed deposit, earning an interest rate of $6\%$ per annum, compounded monthly. The fixed deposit was set to mature on $1$ January $2021.$

Required:

Determine how much money was in the fixed deposit account on $1$ January $2021.$

$(5$ marks$)$

b$)$ You intend to accumulate R$98000$ in a fixed deposit account at the end of eight years. Assuming an interest rate of $7\%,$ calculate the present value of the fixed deposit.

$(5$ marks$)$

c$)$ After working for your employer for eight years, you decided to start your own business. You have determined the initial capital outlay for your new business to be R$280000.$ The new business will be financed from your previous savings, which would have amounted to R$70000$ at the time of starting the new business, and the balance through a bank loan, on which you will have to make annual repayments at the end of each year over five years.

Required:

i$)$ Assuming an interest rate of $8\%($annual compounding$),$ calculate the amount you will need to pay at the end of each year to repay the loan.

$(9$ marks$)$

ii$)$ Determine how much interest you will have paid to the bank at the end of the eight years.

$(4$ marks$)$

Show all calculations and round all factors to $3$ decimal places.