Jerry receives R12 000 to invest for a period of 5 years - NSC Mathematics - Question 6 - 2016 - Paper 1

To calculate the future value (FV) of the investment, we use the formula:

$FV = P \times (1 + \frac{r}{n})^{nt}$

Where:

• P = principal amount (R12,000)
• r = nominal interest rate (0.085)
• n = number of compounding periods per year (4)
• t = time in years (5)

Plugging in the values:

$FV = 12000 \times \left(1 + \frac{0.085}{4}\right)^{4 \times 5}$

Simplifying this:

$FV = 12000 \times \left(1.02125\right)^{20}$

Therefore:

$FV = 12000 \times 1.4859 \approx R17830.68$

Thus, the amount Jerry will receive at the end of 5 years is approximately R17,830.68.

Using the formula for depreciation under the reducing-balance method:

$V = P(1 - r)^t$

Where:

• V = final value (R41,611.57)
• P = initial cost (R120,000)
• r = rate of depreciation (12.4% or 0.124)
• t = time in years

Rearranging gives:

$t = \frac{\log(V / P)}{\log(1 - r)}$

Plugging in the values:

$t = \frac{\log(41611.57 / 120000)}{\log(1 - 0.124)}$

Thus:

$t = \frac{\log(0.346}{\log(0.876)} \approx 3.79 \text{ years}$

Therefore, it will take approximately 4 years for the furniture to depreciate to R41,611.57.

To find the annual deposit required, we use the future value of an ordinary annuity formula:

$FV = PMT \times \frac{(1 + r)^n - 1}{r}$

Rearranging for PMT:

$PMT = \frac{FV \times r}{(1 + r)^n - 1}$

Here:

• FV = R20,000
• r = 2% (quarterly rate of 8% p.a. is $\frac{0.08}{4} = 0.02$)
• n = 12 (3 years with quarterly compounding)

Substituting values, we get:

$PMT = \frac{20000 \times 0.02}{(1 + 0.02)^{12} - 1}$

Therefore:

$PMT = \frac{400}{(1.02)^{12} - 1} \approx 31.89$

Thus, Andrew must deposit approximately R31.89 at the beginning of each year.