Question $4.$

$4\mathrm{.}1$ When John purchased his new car, the bank offered him a loan at a effective rate of $16,4\%$ p$.$a$.$ What was the nominal interest rate, compounded monthly, he was required to pay? $(4)$

$4\mathrm{.}2$ Simone's grandmother plans to give her R$50000$ on her $21$st birthday. She takes out an annuity which offers interest of $8,2\%$ p$.$a$.$ compounded monthly. If she starts paying into the annuity on Simone's $10$th birthday, and stops her contributions one month before Simone turns $21,$ what must her monthly contributions be so that Simone receives R$50000$ on her $21$st birthday?

$(5)$

$4\mathrm{.}3$ Ernest takes out a twenty year loan of R$100000.$ He repays the loan by means of equal monthly payments starting three months after the granting of the loan. The interest rate is $18\%$ per annum compounded monthly.

$4\mathrm{.}3\mathrm{.}1$ Calculate the amount owing two months after the loan was taken out by Ernest. $(3)$

$4\mathrm{.}3\mathrm{.}2$ Calculate the monthly repayments. The $20-$year period starts on the day the loan started.

Total: $15$ marks

Question $5.$Question $4.$

$4\mathrm{.}1$ When John purchased his new car, the bank offered him a loan at a effective rate of $16,4\%$ p$.$a$.$ What was the nominal interest rate, compounded monthly, he was required to pay? $(4)$

$4\mathrm{.}2$ Simone's grandmother plans to give her R$50000$ on her $21$st birthday. She takes out an annuity which offers interest of $8,2\%$ p$.$a$.$ compounded monthly. If she starts paying into the annuity on Simone's $10$th birthday, and stops her contributions one month before Simone turns $21,$ what must her monthly contributions be so that Simone receives R$50000$ on her $21$st birthday?

$(5)$

$4\mathrm{.}3$ Ernest takes out a twenty year loan of R$100000.$ He repays the loan by means of equal monthly payments starting three months after the granting of the loan. The interest rate is $18\%$ per annum compounded monthly.

$4\mathrm{.}3\mathrm{.}1$ Calculate the amount owing two months after the loan was taken out by Ernest. $(3)$

$4\mathrm{.}3\mathrm{.}2$ Calculate the monthly repayments. The $20-$year period starts on the day the loan started.

Total: $15$ marks

Question $5.$