## Exam Style Question## Worked solutions to typical exam type questions that you can reveal gradually |

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.

The worked solutions to these exam-style questions are only available to those who have a Transum Subscription. Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves. This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures. A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience. |

Drag this panel down to reveal the solution

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

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

©1997 - 2017 Transum Mathematics :: For more exam type questions and worked solutions go to Transum.org/Maths/Exam/