2020 Nov P1 Q6

Question 6

$6.1$	On $31$ January $2020$ , Tshepo made the first of his monthly deposits of $R1\,000$ into a savings account. He continues to make monthly deposits of $R1\,000$ at the end of each month up until $31$ January $2032$ . The interest rate was fixed at $7,5\%$ p.a., compounded monthly.
$\quad 6.1.1$	What will the investment be worth immediately after the last deposit?	$(4)$
$\quad 6.1.2$	If he makes no further payments but leaves the money in the account, how much money will be in the account on $31$ January $2033$ ?	$(2)$
$6.2$	Jim bought a new car for $R250\,000$ . The value of the car depreciated at a rate of $22\%$ p.a. annually according to the reducing-balance method. After how many years will its book value be $R92\,537,64$ ?	$(3)$
$6.3$	Mpho is granted a loan under the following conditions: The interest rate is $11,3\%$ p.a., compounded monthly. The period of the loan is $6$ years. The monthly repayment on the loan is $R1\,500$ . Her first repayment is made one month after the loan is granted.
$\quad 6.3.1$	Calculate the value of the loan.	$(3)$
$\quad 6.3.2$	How much interest will Mpho pay in total over the first $5$ years?	$(4)$
		$\textbf{[16]}$