Diane invests a lump sum of R5 000 in a savings account for exactly 2 years - NSC Mathematics - Question 7 - 2016 - Paper 1

To calculate the amount in Diane's savings account, we can use the formula for compound interest:

$A = P(1 + i)^n$

Where:

• $P = 5000$ (initial investment)
• $i = 0.025$ (quarterly interest rate)
• $n = 8$ (total quarters in 2 years)

Now substituting the values:

$A = 5000(1 + 0.025)^{8} = 5000(1.025)^{8} = R6 092.01$

Therefore, the amount in Diane’s account at the end of 2 years is R6 092.01.

To find the total number of withdrawals, we first need to calculate the balance after exceeding withdrawals each month until the fund is depleted. The formula for the present value of annuity can be applied:

$P = \frac{A \cdot (1 - (1 + i)^{-n})}{i}$

Where:

• $P = 800000$, total investment
• $A = 10000$, withdrawal amount
• $i = \frac{0.14}{12}$, monthly interest rate

Setting this up gives:

$800000 = \frac{10000 \cdot (1 - (1 + \frac{0.14}{12})^{-n})}{\frac{0.14}{12}}$

Solving for $n$ yields approximately 233 withdrawals.

To calculate the value of Motloli's deposit after 4 years, we can again use the compound interest formula, with updated values:

$A = P(1 + i)^{n}$

The values are:

• $P = 800000$ (initial investment)
• $i = \frac{0.14}{12}$
• $n = 48$ (total months in 4 years)

Calculating this gives:

$A = 800000(1 + \frac{0.14}{12})^{48} = R757428$

Thus, Motloli's deposit value is R757428.

Given that Motloli's deposit is 30% of the purchase price, we can express this as:

$y = \frac{757428}{0.30}$

Calculating the purchase price:

$y = R2 524 760$

Therefore, the purchase price of the house is R2 524 760.