7.1 A company bought a new machine for R500 000. After 3 years, the machine has a book value of R331 527. Calculate the yearly rate of depreciation if the machine was depreciated according to the reducing-balance method. 7.2 Musa takes a personal loan from a bank to buy a motorcycle that costs R46 000. The bank charges interest at 24% per annum, compounded monthly. How many months will it take Musa to repay the loan, if the monthly instalment is R1 900? 7.3 Neil set up an investment fund. Exactly 3 months later and every 3 months thereafter he deposited R3 500 into the fund. The fund pays interest at 7.5% p.a., compounded quarterly. He continued to make quarterly deposits into the fund for 6½ years from the time that he originally set up the fund. Neil made no further deposits into the fund, but left the money in the same fund at the same rate of interest. Calculate how much he will have in the fund 10 years after he originally set it up.

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7.1 A company bought a new machine for R500 000 - NSC Mathematics - Question 7 - 2017 - Paper 1

Question 7

7.1 A company bought a new machine for R500 000. After 3 years, the machine has a book value of R331 527. Calculate the yearly rate of depreciation if the machine wa... show full transcript

Worked Solution & Example Answer:7.1 A company bought a new machine for R500 000 - NSC Mathematics - Question 7 - 2017 - Paper 1

Step 1

7.1 Calculate the yearly rate of depreciation

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Answer

To find the yearly rate of depreciation using the reducing-balance method, we utilize the formula:

$A = P(1-i)^n$

Where:

$A$ = book value after $n$ years
$P$ = initial cost of the machine
$i$ = depreciation rate
$n$ = number of years

In this case:

$A = R331527$
$P = R500000$
$n = 3$

Plugging in these values, we rearrange the formula to find $i$ :

$331527 = 500000(1-i)^3$

Dividing both sides by 500000 gives:

$rac{331527}{500000} = (1-i)^3$

Taking the cube root and manipulating the equation will yield:

$1-i = rac{331527^{1/3}}{500000^{1/3}}$

Finally, solving for $i$ :

Approximately $i = 0.12800$ or $12.8\%$ .

Step 2

7.2 How many months will it take Musa to repay the loan?

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Answer

To calculate the number of months it will take for Musa to repay his loan, we use the formula for the monthly payment:

$P = rac{X(1 + i)^n}{(1 + i)^n - 1}$

Where:

$P = R1900$ (monthly instalment)
$X = R46000$ (loan amount)
$i = rac{0.24}{12} = 0.02$ (monthly interest rate)
$n$ = number of months

Rearranging gives:

$n = rac{- ext{log}igg(1 - rac{iX}{P}igg)}{ ext{log}(1+i)}$

Substituting in $X$ , $P$ , and $i$ :

$n = rac{- ext{log}igg(1 - rac{0.02 imes 46000}{1900}igg)}{ ext{log}(1 + 0.02)}$

Calculating this will yield approximately 34 months.

Step 3

7.3 Calculate the fund value after 10 years.

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Answer

To find how much Neil will have in the fund 10 years after starting, we calculate the future value of an investment with regular deposits:

The future value $F$ of an investment can be calculated as:

$F = X \left(\frac{(1+i)^n - 1}{i}\right)$

Where:

$X = R3500$ (quarterly deposit)
$i = rac{0.075}{4} = 0.01875$ (quarterly interest rate)
$n = 4\times 6.5 = 26$ (total number of deposits)

Calculating gives:

Calculate $F$ after the last deposit:

$F_{after\,last} = 3500 \left(\frac{(1 + 0.01875)^{26} - 1}{0.01875}\right)$

This yields:

$F_{after\,last} \approx R115902.61$

Now, we need to consider the remaining 4 years (or 16 quarters) without additional deposits:

$F = 115902.61(1 + 0.01875)^{16}$

Calculating gives:

$F \approx R150328.12$

Therefore, Neil will have approximately R150328.12 in the fund after 10 years.

7.1 A company bought a new machine for R500 000 - NSC Mathematics - Question 7 - 2017 - Paper 1

Worked Solution & Example Answer:7.1 A company bought a new machine for R500 000 - NSC Mathematics - Question 7 - 2017 - Paper 1

7.1 Calculate the yearly rate of depreciation

7.2 How many months will it take Musa to repay the loan?

7.3 Calculate the fund value after 10 years.

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