$1.$ Harry's financial advisor has informed him that he will have a shortfall of R$1,400,000\mathrm{.}00$ in retirement capital when he retires in $18$ years' time. Harry wants to invest by way of annual instalments that he will make at the beginning of every year. The instalments must increase annually in line with his salary increase, which he anticipates will be $6\%$ per annum. His financial advisor advised him to invest in a fund that will grow at $9\%$ per annum. Calculate the first instalment that Harry must invest now $($the beginning of the first year$).$ Choose the closest correct option.

a$.$ R$20,685\mathrm{.}00$

b$.$ R$21,271\mathrm{.}00$

c$.$ R$20,564\mathrm{.}00$

d$.$ R$21,129\mathrm{.}00$

e$.$ None of the above

$2.$ Christi got a loan from a bank to purchase a house ten years ago. The loan was for an amount of R$2,500,000\mathrm{.}00.$ The loan's repayment term is $20$ years, and the interest rate is $7\mathrm{.}6\%$ annually. The instalments are payable monthly in arrears. The outstanding period of the loan is ten years. The bank informed her that her interest rate was increased to $12\mathrm{.}6\%$ for the remaining ten years. She would like to increase her monthly instalment so the loan will be fully paid off in seven years' time. To do this, her new monthly instalment will be$?$ Choose the closest correct option.

a$.$ R$26,026\mathrm{.}00$ per month

b$.$ R$30,087\mathrm{.}00$ per month

c$.$ R$25,862\mathrm{.}00$ per month

d$.$ R$30,595\mathrm{.}00$ per month

e$.$ None of the above

$3.$ Hester has an amount of R$3,313,023\mathrm{.}00$ that she wants to invest for a four$-$year term in a fixed interest rate investment. She can invest the amount in a term deposit with ABC Bank Ltd$.$ It is for a term of four years, and interest accrues monthly. The nominal rate of interest is $10\mathrm{.}25\%.$ What will the effective interest rate be$?$ Choose the closest correct option.

a$.10\mathrm{.}89\%$

b$.10\mathrm{.}48\%$

c$.10\mathrm{.}75\%$

d$.10\mathrm{.}32\%$

e$.$ None of the above

$4.$ Mark is a member of a pension fund. He will retire from the fund in $12$ years' time. The current value of his interest in the fund is R$2,550,000\mathrm{.}00.$ He and his employer each contribute $8\%$ of his salary of R$600,000\mathrm{.}00$ per annum to the fund. His salary will increase by the rate of inflation of $6\%$ every year. Use a fund growth rate of $9\%$ per annum. What will the value of his interest upon retirement in twelve years' time be$?$ Choose the closest correct option.

a$.$ R$9,964,327\mathrm{.}00$

b$.$ R$9,887,482\mathrm{.}00$

c$.$ R$9,214,103\mathrm{.}00$

d$.$ R$7,634,134\mathrm{.}00$

e$.$ None of the above

$5.$ Shaun took out a loan with a bank eight years ago. The loan was for an amount of R$1,500,000\mathrm{.}00,$ the interest rate was $8\mathrm{.}5\%$ per annum, and the full term of the loan was ten years. The remaining term is currently two years. The bank has now reduced the interest rate to $8\mathrm{.}1\%$ per annum. Calculate Sean's new reduced monthly instalment for the remaining two years. Choose the closest correct option.

a$.$ R$18,252\mathrm{.}00$ per month

b$.$ R$18,399\mathrm{.}00$ per month

c$.$ R$18,269\mathrm{.}00$ per month

d$.$ R$18,523\mathrm{.}00$ per month

e$.$ None of the above

$6.$ Werner passed away on $01$ June $2023.$ His life insurance policy paid out an amount of R$5,000,000\mathrm{.}00$ as a death benefit. His $12-$year$-$old daughter, the policy beneficiary, will receive monthly payments. The first payment is on $01$ July $2023.$ His daughter will receive level monthly payments until she is $25$ years old, and interest will be earned at $8\%.$ Calculate the value of this payment and choose the closest correct option.

a$.$ R$51,312\mathrm{.}00$

b$.$ R$54,123\mathrm{.}00$

c$.$ R$51,654\mathrm{.}00$

d$.$ R$53,764\mathrm{.}00$

e$.$ None of the above

$7.$ Reitumetsi took a loan of R$1,500,000\mathrm{.}00$ five years ago. The annual interest rate is $13\mathrm{.}0\%$ per annum, the term $20$ years, of which $15$ years remain. She just inherited an amount of R$300,000\mathrm{.}00$ and has been advised by her financial advisor to take the inheritance and repay a portion of her loan. The bank has also informed her that the interest rate on her loan increased from $13\%$ to $13\mathrm{.}5\%$ with immediate effect $($from the beginning of month $61).$ Calculate the new monthly instalment if Reitumetsi decides to use $75\%$ of her inheritance towards paying off the loan and with the new rate change: Choose the closest correct option.

a$.$ R$14,138\mathrm{.}00$

b$.$ R$13,790\mathrm{.}00$

c$.$ R$15,112\mathrm{.}00$

d$.$ R$14,753\mathrm{.}00$

e$.$ None of the above

$8.$ Mary invests an amount of R$1,000,000\mathrm{.}00$ for a period of ten years. She will earn interest of $11\mathrm{.}2\%$ per annum, accumulating quarterly. She will pay income tax at a rate of $45\%$ on the interest. Ignore any income tax exemptions in respect of interest. What will her effective after$-$tax rate of return be$?$ Use four decimal places for the calculation. Choose the closest correct option.

a$.5\mathrm{.}7385\%$

b$.5\mathrm{.}1361\%$

c$.6\mathrm{.}3038\%$

d$.6\mathrm{.}1423\%$

e$.$ None of the above

$9.$ Six years ago, Garry obtained a loan of R$485,000\mathrm{.}00$ from ABC Bank Ltd at an interest rate of $13\mathrm{.}75\%$ per annum. The loan has a total repayment term of $17$ years. The instalments are payable at the end of every month. The remaining term is $11$ years. Garry will retire in eight years' time and wants to increase his monthly instalments to make sure that the loan is fully repaid on his retirement date. Calculate the new increased monthly instalmen