## Miscellaneous Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. The questions selected here all contain the text 'Interest'. |

## 1. | GCSE Higher |

Winky Lash wants to invest £20 000 for 3 years in a bank. She has the following two choices of banks, both offering compound interest but on different terms:

## Leftway Bank1% AER |
::-:: | ## Righton Bank2.1% for the first year |

Which bank will give Winky the most interest at the end of the three years?

Show all of your working.

## 2. | GCSE Higher |

Michael Banks invests £2000 in a savings account for two years. The account pays 2% compound interest per annum.

Michael has to pay 15% tax on the interest earned each year. This tax is taken from the account at the end of each year.

How much money will Michael have in his account at the end of the two years? Give your answer to the nearest penny.

## 3. | GCSE Higher |

Here are the details for two bank accounts.

Dayter Bank

2% per year compound interest.

No withdrawals until the end of three years.

Rivver Bank

3% interest for the first year

2% for the second year

1% for the third year.

Withdrawals allowed at any time.

Saviour has £2000 he wants to invest.

(a) Calculate, to the nearest penny, which bank would give him most money if he invests his money for 3 years.

(b) Explain why he might not want to use Dayter Bank.

## 4. | GCSE Higher |

Montague invests £7000 for six years in a bank offering compound interest at \(x%\) per annum.

The investment is worth £7654.10 at the end of the six years.

Find the value of \(x\).

## 5. | IB Studies |

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.

## 6. | IB Applications and Interpretation |

Mr and Mrs Moule are considering purchasing a new car with a price of £12000

The dealership offers two options to finance a loan.

A five year loan at a nominal annual interest rate of 12 % compounded quarterly. No deposit is required and repayments are made each quarter.

(a) Find the repayment made each quarter.

(b) Find the total amount that will have been paid for the car by the end of the five years.

(c) Find the total amount interest that will have been paid on the loan by the end of the five years.

A five year loan at a nominal annual interest rate of \(r\)% compounded monthly. An Initial 12% deposit is required and monthly repayments of £255.

(d) Find the annual interest rate, \(r\).

(e) State which option Mr and Mrs Moule should choose and justify your answer.

This new car will depreciates at an annual rate of 20% per year.

(f) Find the value of Mr and Mrs Moule’s car when it is ten years old.

## 7. | IB Studies |

All answers to this question should be given to the nearest whole currency unit.

Katie and Keith each have 9000 USD to invest.

Katie invests her 9000 USD in a bank account that pays a nominal annual interest rate of 3.8% compounded yearly. Keith invests his 9000 USD in an account that offers a fixed interest of 410 USD each year.

(a) Find the amount of money that Keith will have in the bank after 4 years.

(b) Find the amount of money that Katie will have in the bank at the end of 9 years.

(c) Find the number of complete years it will take for Katie’s investment to first exceed 12000 USD.

(d) Find the number of complete years it will take for Katie’s investment to exceed Keith’s investment.

Keith moves from the USA to Spain. He transfers 3500 USD into a Spanish bank which has an exchange rate of 1 USD = 0.89 euros. The bank charges 1.5% commission.

(e) Calculate the amount of money Keith will invest in the Spanish bank after commission.

Keith returns to the USA for a short holiday. He converts 900 euros at a bank in Rutherford, NJ and receives 1018.44 USD. The bank advertises an exchange rate of 1 euro = 1.15 USD.

(f) Calculate the percentage commission Keith is charged by the bank.

## 8. | IB Studies |

Christine owns a four sided piece of land shown in the diagram below as ABCD. The length of BC is 180 m, the length of CD is 70 m, the length of AD is 90 m, the size of angle BCD is 82° and the size of angle BAD is 102°. The diagram is not to scale

Christine decides to sell the triangular portion of land ABD. She first builds a straight fence from B to D.

(a) Calculate the length of the fence.

The fence costs 19 USD per metre to build.

(b) Calculate the cost of building the fence. Give your answer correct to the nearest USD.

(c) Show that the size of angle ABD is 28.6°, correct to three significant figures.

(d) Calculate the area of triangle ABD.

She sells the land for 110 USD per square metre.

(e) Calculate the value of the land that Christine sells. Give your answer correct to the nearest USD.

Christine invests 200 000 USD from the sale of the land in a bank that pays compound interest compounded annually.

(f) Find the interest rate that the bank pays so that the investment will double in value in 12 years.

## 9. | IB Applications and Interpretation |

The 2nd Rutherford American Scouts joined the 37th Wolverhampton British Scouts for an International Camp. Skipper Jones is interested to see if the mean height of American Scouts, \( \mu_1\), is the same as the mean height of British Scouts, \( \mu_2\). The information is recorded in the following table.

American Scout height (cm) | 147 | 153 | 151 | 142 | 155 | 149 | 154 | 156 | 143 | 152 | 149 | 158 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

British Scout height (cm) | 142 | 146 | 155 | 145 | 149 | 148 | 152 | 143 | 147 | 150 | 149 | 154 | 150 | 144 | 146 |

At the 10% level of significance, a t-test was used to compare the means of the two groups. The data is assumed to be normally distributed and the standard deviations are equal between the two groups.

(a) State the null hypothesis.

(b) State the alternative hypothesis.

(c) Calculate the p-value for this test.

(d) State, giving a reason, whether Skipper Jones should accept the null hypothesis.

## 10. | IB Analysis and Approaches |

Ruby invests a certain amount of money in a bank account that pays a nominal annual interest rate of 6.7%, compounded quarterly.

The amount of money in Ruby’s account at the end of each year forms a geometric sequence with common ratio, r.

(a) Find the value of the Annual Equivalent Rate (AER) represented by r.

(b) If Ruby invested her money on the 1st January 2022, find the year in which the amount of money in Ruby's account will become three times the amount she invested.

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