I need some help with this question, My answer to question E) is 1880 pounds per year, can anyone suggest a different answer, also does anyone know how would I revise for questions of this type.

Give answers, where appropriate, to 1 decimal place.

Julia Parsons runs a small business hiring out canoes and pedaloes (pedal boats) in a seaside holiday resort during the summer months. The canoes and pedaloes are subjected to considerable “wear and tear”.

Julia’s “fleet” consists of

  • 10 single canoes (canoes for a single person)
  • 12 double canoes (canoes for 2 persons)
  • 12 pedaloes (pedal boats)
  • 2 large canoes (canoes for 4 persons)

The hiring costs per hour for these are,
Single £4;
Double £6;
Pedaloes £3;
Large £8

Julia has kept a record of usage over several years and assesses the total usage according to the following table.

Table 1 Number of occasions when canoe/pedalo is hired for the period shown

Due to the heavy “wear and tear” each pedalo has to be replaced every 3 years and each canoe every 5 years. Julia maintains a depreciation fund for this purpose and puts the same amount of money each year in to this fund. The costs for new are,
Single £200;
Double £230;
Pedaloes £150;
Large £400

(e) How much does Julia put in to the fund each year?

  • $\begingroup$ By my calculations the replacement cost averages £1712 a year: in a 15-year span she must replace 30 single canoes, 36 double canoes, 60 pedaloes, and 6 large canoes, at a total cost of £25680. Putting in £1712 a year is therefore a steady-state solution. However, it’s not enough starting from scratch, because at the end of 6 years she’s had to pay £12920 and has deposited only £10272. $\endgroup$ Feb 18, 2012 at 23:23
  • $\begingroup$ Ignore that last sentence: the £12920 figure is wrong. $\endgroup$ Feb 18, 2012 at 23:48
  • $\begingroup$ Table 1 is missing. . . How can we answer this if we don't know "number of occasions when canoe/pedalo is hired for the period shown"? That affects the answer entirely. $\endgroup$
    – 000
    Feb 19, 2012 at 0:26

2 Answers 2


If a single canoe lasts 5 years and costs 200, you need to add 200/5=40 to the depreciation fund for each boat, or 400/year for the fleet of 10. The others are similar: 230*12/5=552 for double canoes, 150*12/3=600 for pedaloes, 2*400/5=160 for large canoes (assuming they last 5 years), giving me 1712. If the large canoes last only 3 years, they need 266.7 per year, giving 1818.7


You can work out the annual replacement costs, as Ross did in his answer, or you can first work out the total replacement cost over a convenient period, as I did in my comment. Since $15$ is the least common multiple of $3$ and $5$, $15$ years is a convenient period: each pedalo must be replaced $5$ times, and each canoe $3$ times. Thus, the total replacement cost in pounds is

$$5\cdot 150\cdot 12+3\Big(200\cdot 10+230\cdot 12+400\cdot 2\Big)=25680$$

over $15$ years, or $\dfrac{25680}{15}=1712$ pounds a year.

This answer assumes that the depreciation fund does not earn interest, since nothing is said about interest in the problem. And contrary to what I said in my comment, the fund is always sufficient to cover the replacement costs. Assuming that the replacement fund starts at $0$, here’s a table of the total replacement costs and the amount in the fund at the points at which craft are replaced:

$$\begin{array}{r|r|r} \text{Year}&\text{Total Costs}&\text{Paid to Fund}\\ \hline 0&0&0\\ 3&1800&5136\\ 5&7360&8560\\ 6&9160&10272\\ 9&10960&15408\\ 10&16520&17120\\ 12&18320&20540\\ 15&25680&25680 \end{array}$$


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