Calculate the accumulated amount in this account on Mary's 16th birthday. After 4 years, the value of a printer was half of its original value. Determine the rate at which the value of the printer depreciated over this period, if depreciation was calculated according to a straight-line method.

Step 1: Identify the given values and determine the number of periods and periodic interest rate. The future value (FV) Sarah wishes to accumulate is R10 000 000. The nominal annual interest rate ($i_{nom}$) is 15% or $0.15$. The interest is compounded monthly, so the compounding frequency (m) is 12. The monthly interest rate ($i$) is calculated as: $i = \frac{i_{nom}}{m} = \frac{0.15}{12} = 0.0125$ Sarah starts making payments on her 18th birthday and the last payment is one month before her 50th birthday. This means payments are made for $50 - 18 = 32$ years. The total number of monthly payments (n) is: $n = 32 years \times 12 months/year = 384 \text{ months}$

Step 2: Apply the future value of an ordinary annuity formula. The formula for the future value of an ordinary annuity is: $FV = P \left[ \frac{(1+i)^n - 1}{i} \right]$ Where P is the monthly instalment. Substitute the known values into the formula: $10,000,000 = P \left[ \frac{(1+0.0125)^{384} - 1}{0.0125} \right]$

Step 3: Calculate the term inside the brackets. First, calculate $(1+0.0125)^{384}$: $(1.0125)^{384} \approx 117.3248006$ Now, substitute this back into the bracketed term: $\frac{117.3248006 - 1}{0.0125} = \frac{116.3248006}{0.0125} \approx 9305.984048$

Step 4: Solve for P, the monthly instalment. $10,000,000 = P \times 9305.984048$ $P = \frac{10,000,000}{9305.984048}$ $P \approx 1074.57$

The monthly instalment Sarah will make is: $\boxed{R1074.57}$