A company bought a photocopier for R150 000 on 1 July 2022 - NSC Mathematics - Question 6 - 2023 - Paper 1

To calculate the trade-in value using straight-line depreciation, we can use the formula:

$S = P - (D \times n)$

Where:

• $S$ is the salvage value (trade-in value).
• $P$ is the original cost of the old photocopier (R150 000).
• $D$ is the depreciation per year (9% of the original cost).
• $n$ is the number of years (5).

Calculating $D$:

$D = 0.09 \times 150000 = R13 500$

Now substituting back into the salvage value equation:

$S = 150000 - (13500 \times 5) = 150000 - 67500 = R82 500$

To find the monthly deposit amount, we use the future value of an ordinary annuity formula:

$F = P \times \frac{(1 + i)^n - 1}{i}$

Where:

• $F$ is the future value (R123 013).
• $P$ is the monthly payment.
• $i$ is the monthly interest rate (annual rate / 12).
• $n$ is the total number of payments (12 months/year \times 5 years).

First, we determine $i$ and $n$:

• $i = \frac{0.0785}{12} = 0.00654$
• $n = 12 \times 5 = 60$

Now substituting into the future value formula and solving for $P$:

$123013 = P \times \frac{(1 + 0.00654)^{60} - 1}{0.00654}$

Calculating:

$P \approx R1 704.01$