2019 Nov P1 Q6

Question 6

6.1

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:

\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]}

Question 6

$6.1$	Two friends, Kuda and Thabo, each want to invest $R5\,000$ for four years. Kuda invests his money in an account that pays simples interest at $8,3\%$ per annum. At the end of four years, he will receive a bonus of exactly $4\%$ of the accumulated amount. Thabo invests his money in an account that pays interest at $8\%$ p.a., compounded monthly.
	Whose investment will yield a better return at the end of four years? Justify your answer with appropriate calculations.	$(5)$
$6.2$	Nine years ago, a bank granted Mandy a home loan of $R525\,000$ . This loan was to be repaid over $20$ years at an interest rate of $10\%$ p.a., compounded monthly. Mandy's monthly repayments commenced exactly one month after the loan was granted.
$\quad 6.2.1$	Mandy decided to make monthly repayments of $R6\,000$ instead of the required $R5\,066,36$ . How many payments will she make to settle the loan?	$(5)$
$\quad 6.2.2$	After making monthly repayments of $R6\,000$ for nine years, Mandy required money to fund her daughter's university fees. She approached the bank for another loan. Instead, the bank advised Mandy that the extra amount repaid every month could be regarded as an investment and that she could withdraw this full amount to fund her daughter's studies. Calculate the maximum amount that Mandy may withdraw from the loan account.	$(4)$
		$\textbf{[14]}$

$6.1$	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?	$(4)$
		$\textbf{[16]}$