 # Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

GCSE Higher

Elaine invests £150 000 in a savings account for six years.

The account pays compound interest at a rate of 1.2% per annum.

Calculate the total amount of interest Elaine will get at the end of the six years to the nearest pound.

### 2.

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

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

### 3.

GCSE Higher

The value of a boat is £220 000.

Each year the value decreases by 12% of the value at the beginning of that year.

Work out the value of the boat after four years have passed.

### 4.

GCSE Higher

The value of a new car is £22 000.

The value of the car decreases by 30% in the first year then 10% in each of the next 5 years.

Work out the value of the car after 6 years.

### 5.

GCSE Higher

Using $$x_{n+1}=-5-\frac{6}{x_n^2}$$

with $$x_0 = -1.5$$

(a) find the values of $$x_1, x_2$$ and $$x_3$$

(b) Explain the relationship between the values of $$x_1, x_2$$ and $$x_3$$ and the equation $$x^3+5x^2+6=0$$

### 6.

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.

### 7.

GCSE Higher

The value of a new house, $$V$$, is given by:

$$V = 120000 × 1.1^t$$

where t is the age of the house in complete years and V is in pounds.

(a) Write down the value of V when t = 0.

(b) What is the value of V when t = 4?

(c) After how many complete years will the house’s value rise above £200 000?

### 8.

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.

### 9.

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 $$x$$.

### 10.

GCSE Higher

Consider the following cubic equation:

$$x^3-7x-5=0$$

An approximate solution can be found by using the following iterative process.

$$x_{n+1}=\frac{(x_n)^3-5}{7}$$

(a) Find $$x_2$$ and $$x_3$$ if $$x_1=-1$$

Work out the solution to 6 decimal places.

### 11.

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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