This chapter is about problem solving in general rather than about the mechanics of any particular type of question. The following questions however remind you of the useful techniques you have encountered there.

You wish to borrow a certain sum of money at 8% per annum. How frequently would you prefer the interest to be compounded?

You wish to invest a certain sum of money at 8% per annum. How frequently would you prefer the interest to be compounded?

You have been asked to solve a practical problem for your company. You should consider your part in the problem solving exercise to be complete:

You have been asked by your company to help towards solving a problem. They have presented you with a large quantity of numerical data related to the problem. Which of the following pairs of techniques are most likely to be of use to you?

£2000 is invested for 5 years at 12% per annum. If compounded annually its value after 5 years is:

£2000 is invested for 5 years at 1% per month. Its value after 5 years is:

The interest earned by the money in Question 6 is:

A credit card charging 2% per month is used to buy an item costing £1000. If the debt remains unpaid for a year, how much will it be?

What would the annual interest rate be to produce the same debt at the end of the year as in Question 7?

You are saving up to buy a new car. You estimate that it will cost you £15 000 in 5 years time and you assume that the interest will stay at 6% per annum. (Information for questions 10 – 13.)

How much will you need to invest as a lump sum now in order to reach your target?

If you make 5 annual payments starting now, how much will each annual payment need to be?

How much will your car fund be worth in three years time?

Your friend wants to save up for the same car but can only afford £2000 p.a.
For how many years will he have to save, assuming that the car remains the same price and that the interest rate is still 6% p.a.?

A company expects to buy new printing equipment every 4 years. The new equipment will cost £12 000. (Information for questions 14 – 16)

If the trade in value after 4 years is only £4000, what is the annual straight line depreciation?

What would be the percentage depreciation in the first year?

What would be the percentage depreciation in the fourth year?

After 10 years the value of an investment is £3 238. If the interest had been compounded at 8% per annum, what was the original amount invested?

What is the present value of a payment of £4000 which is to be made in 6 years time, if we assume the invested money earns compound interest at 5%?

A car manufacturer needs to revise its stock keeping policy in order to minimise costs. At the moment they receive a regular order of 300 cases of 100 tyres of a particular size per month with a fixed delivery charge of £100 plus £5 per case. The stock holding cost for these tyres is calculated to be £5 per case per month. Use this information to answer Questions 19 – 24.

What is their total annual cost of ordering and storing these tyres at present?

You need to solve a problem relating the total stock ordering and holding cost to the quantity ordered for each delivery. A good choice for the names of the variables would be:

The car manufacturer wishes to alter the quantity (q) of cases of tyres ordered so that they can minimise their total costs (£C). All other values include the annual demand remain constant.

The formula for the annual cost of placing their orders is:

The formula for the total cost is:

The order size (number of containers) to be used to minimise costs is:

The total cost of ordering and storing these tyres is now:

A manufacturer has fixed costs of £300 plus £2 per item manufactured. The demand (x) for his product is related to the price (£p): it has a theoretical maximum value of 600 but reduces by 50 for every £1 charged.

The formula for the demand (x) is:

The formula for his total costs is:

The formula for his total revenue is:

The demand at break-even point when costs and revenue are equal is:

The total cost at the break-even point at which the company starts to make a profit is:

The total revenue at the break-even point is: