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On the 2nd day of January 2015 a company bought a new printer for R150 000 - NSC Mathematics - Question 6 - 2017 - Paper 1
Question 6
On the 2nd day of January 2015 a company bought a new printer for R150 000. The value of the printer decreases by 20% annually on the reducing-balance method. When ... show full transcript
Worked Solution & Example Answer:On the 2nd day of January 2015 a company bought a new printer for R150 000 - NSC Mathematics - Question 6 - 2017 - Paper 1
Step 1
Calculate the book value of the printer on the 2nd day of January 2017
Answer
To calculate the book value after two years of depreciation of 20% per year, we use the formula for reducing balance:
Where:
- is the book value.
- is the initial price (R150,000).
- is the depreciation rate (0.20).
- is the number of years.
Calculate:
Step 2
At the beginning of which year will the company have to replace the printer? Show ALL calculations.
Answer
To find when to replace the printer, we stay with the reducing-balance method:
We need to find when the book value drops to R49,152:
Dividing both sides:
rac{49152}{150000} = (0.8)^n
Calculating the left-hand side:
Taking logarithm on both sides:
Solving for :
≈ 5$$ Thus, the printer will be replaced at the beginning of the year 2020.Step 3
Calculate the amount that should be deposited every three months to have enough money to replace the printer on 2 January 2020.
Answer
First, calculate the amount needed:
The new printer costs R280,000, and the old printer sells for R49,152. The balance required is:
Now, we use the future value formula for compound interest:
FV = P imes rac{(1 + i)^n - 1}{i}
Where:
- is the future value (R230,848).
- is the deposit amount.
- is the interest rate per period (0.02125, for quarterly interest at 8.5%).
- is the total number of deposits (20 quarters).
Rearranging to solve for P gives:
P = rac{FV imes i}{(1 + i)^n - 1}
By substituting the values:
≈ R9,383.26$$