# Miscellaneous Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams. The questions selected here all contain the text 'compound 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 Bank

1% AER
For investments over
£10 000

::-::

### Righton Bank

2.1% for the first year
0.6% for each additional 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

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.

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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.

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