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Question id: 109. This question is similar to one that appeared in an IB Studies paper in 2014. The use of a calculator is allowed.

On Billy's 16th birthday his parents gave him options of how he might receive his monthly allowance for the next two years.

**Option A** £55 each month for two years.

**Option B** £10 in the first month, £15 in the second month, £20 in the third month, increasing by £5 each month for two years.

**Option C** £15 in the first month and increasing by 10% each month for two years.

**Option D** Investing £1200 at a bank at the beginning of the first year, with an interest rate of 5% per annum, compounded monthly.

Billy does not spend any of his allowance during the two year period.

(a) If Billy chooses Option A, calculate the total value of his allowance at the end of the two year period.

(b) If Billy chooses Option B, calculate the amount of money he will receive in the 15th month.

(c) Calculate the total value of his allowance at the end of the two year period if he chooses Option B.

(d) If Billy chooses Option C, calculate the amount of money Billy would receive in the 15th month.

(e) Find the total value of his allowance at the end of the two year period if he chooses Option C.

(f) If Billy chooses Option D, calculate the total value of his allowance at the end of the two year period.

(g) State which of the options, A, B, C or D, Billy should choose to give him the greatest total value of his allowance at the end of the two year period.

Another bank guarantees Billy an amount of £1650 after two years of investment if he invests $1200 at this bank. The interest is compounded annually.

(h) Calculate the interest rate per annum offered by the bank.

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There is a classic investigation called Aunt Lucy's Legacy which is similar to this question.

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