Question $4$:

After completing more research and calculations you consider the following option. You will make a first repayment of $15\%$ of the loan $($from question $3)$ and then you arrange for you to only start paying the remaining instalments $5$ months after the loan was granted. The bank charges interest at $10,75\%$ compounded monthly. All payments are made on the last day of each month.

$4\mathrm{.}1)$ The assistant bank manager treats the first repayment as a deposit and calculates the monthly repayments as follows.

Deposit $=R11250,00$

:$.$ Loan amount $=R63750,00$

:$.($ Loan $+$ interest $)=($ Repayments $+$ Interest $)$

:$\mathrm{.}63750(1+\frac{0\mathrm{.}1075}{24}{)}^{24}=\frac{x[(1+\frac{0\mathrm{.}1075}{12}{)}^{19}-1]}{\frac{0\mathrm{.}1275}{17}}$

:$.x=R3092,78$

$4\mathrm{.}1)$ Why is it erroneous to consider the first repayment as a deposit?

$4\mathrm{.}2)$ Correct the assistant bank manager's calculation error.