5.1 The annual effective interest rate charged by a financial institution is 6.7% - NSC Technical Mathematics - Question 5 - 2018 - Paper 1

Using the straight-line depreciation formula:
$A = P(1 - i \times n)$
Given that the machine's initial value (P) is R240 000 and it depreciated to half its value (R120 000), we can set up the equation with the depreciation rate (i) as 0.16:
$120000 = 240000(1 - 0.16 \times n)$
Solving for n:
$1 - 0.16n = 0.5\implies 0.16n = 0.5\implies n = 3.125\text{ years}$
Therefore, the depreciated value of the machine at the end of the period is R120 000.

As calculated, using the same formula:
$120000 = 240000(1 - 0.16n)$
When solving the equation, we found that (n = 3.125\text{ years}). Giving the answer to the nearest year, it will take approximately 3 years.

For the first 4 years, the investment grows with an interest rate of 11.2%:
$A = P(1 + i)^n = 400000(1 + 0.112)^{4}$
$= 400000(1.112)^{4}$
Calculating gives approximately R622,283.83.
For the next 3 years with an interest rate of 13%:
$A = 622283.83(1 + 0.13)^{3}$
Calculating this yields R898,781.15.
Thus, the total amount Mr Bohlahe will receive at the end of the investment period is approximately R898,781.15.