 # 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

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.

### 4.

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.

### 5.

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 $$x$$.

### 6.

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.

### 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 Analysis and Approaches

Two friends Arthur and Babette, each set themselves a target of saving £12000. They each have £6800 to invest.

(a) Arthur invests his £6800 in an account that offers an interest rate of 8% per annum compounded annually. Find the value of Arthur's investment after 6 years.

(b) Determine the number of complete years required for Arthur's investment to reach the target.

Babette invests her £6800 in an account that offers an interest rate of $$r$$% per annum compounded monthly, where $$r$$ is set to two decimal places.

(c) Find the minimum value of $$r$$ needed for Babette to reach the target after 15 years.

A third friend Callum wants to reach a £9000 target. He puts £4000 under his mattress where it does not earn any interest. His system is to add more money to his savings regularly. Each year he will add half the amount added in the previous year.

(d) Show that Callum will never reach the target if during the first year he adds £2000.

(e) Find the amount Callum needs to add during the first year in order to reach the target after 8 years.

### 9.

IB Studies

A Grecian amphitheatre was built in the form of a horseshoe and has 22 rows.

The number of seats in each row increase by a fixed amount, $$d$$, compared to the number of seats in the previous row. The number of seats in the fifth row, $$u_5$$, is 58, and the number of seats in the ninth row, $$u_{9}$$, is 86. $$u_1$$ represents the number of seats in the first row.

(a) Write an equation for $$u_5$$ in terms of $$d$$ and $$u_1$$.

(b) Write an equation for $$u_{9}$$ in terms of $$d$$ and $$u_1$$.

(c) Write down the value of $$d$$;

(d) Write down the value of $$u_1$$.

(e) Find the total number of seats in the amphitheatre.

Some time later, a second level was added to increase the amphitheatre’s capacity by another 2590 seats. Each row has five more seats than the previous row. The first row on this level has 82 seats.

(f) Find the number of rows on the second level of the amphitheatre.

### 10.

IB Studies

Chris checks his Twitter account and notices that he received a tweet at 8:00am. At 8:05am he forwards the tweet to four people. Five minutes later, those four people each forward the tweet to four new people. Assume this pattern continues and each time the tweet is sent to people who have not received it before.

The number of new people who receive the tweet forms a geometric sequence:

$$1 , 4 , …$$

(a) Write down the next two terms of this geometric sequence.

(b) Write down the common ratio of this geometric sequence.

(c) Calculate the number of people who will receive the tweet at 8:40am.

(d) Calculate the total number of people who will have received the tweet by 8:40am.

(e) Calculate the exact time at which a total of 5 592 405 people will have received the tweet.

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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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