Simple & Compound Interest, Growth & Decay (AQA GCSE Maths)

Viv wants to invest £2000 for 2 years in the same bank.

At the end of 2 years, Viv wants to have as much money as possible.
Which bank should she invest her £2000 in?

The population of a city increased by 5.2% for the year 2014

At the beginning of 2015 the population of the city was 1 560 000

Lin assumes that the population will continue to Increase at a constant rate of 5.2% each year.

Use Lin's assumption to estimate the population of the city at the beginning of 2017
Give your answer correct to 3 significant figures.

i)  Use Lin's assumption to work out the year in which the population of the city will reach 2000000

[2]

ii) If Lin's assumption about the rate of increase of the population is too low, how might this affect your answer to (b)(i)?

[1]

Katie invests £200 in a savings account for 2 years.

The account pays compound interest at an annual rate of

3.3% for the first year
1.5% for the second year

Work out the total amount of money in Katie's account at the end of 2 years.

Katie travels to work by train.
The cost of her weekly train ticket increases by 12.5% to £225

Katie's weekly pay increases by 5% to £535.50

Compare the increase in the amount of money Katie has to pay for her weekly train ticket with the increase in her weekly pay.

Jack has £15 000 to invest in a savings account for 3 years.

He finds information about two savings accounts.

Jack wants to have as much money as possible in his savings account at the end of the 3 years.

Which of these two savings accounts should he choose?

Ian invested an amount of money at 3% per annum compound interest.
At the end of 2 years the value of the investment was £2652.25

Work out the amount of money Ian invested.

Noah has an amount of money to invest for five years.

Noah wants to get the most interest possible.

Which account is best?
You must show how you got your answer.

At the beginning of 2009, Mr Veale bought a company.
The value of the company was £50 000

Each year the value of the company increased by 2%.

Calculate the value of the company at the beginning of 2017
Give your answer correct to the nearest £100

At the beginning of 2009 the value of a different company was £250 000
In 6 years the value of this company increased to £325 000

This is equivalent to an increase of  each year.

Find the value of .
Give your answer correct to 2 significant figures.

Mia wants to borrow £6000 and repay it, with interest, after two years.

She sees two offers for loans.

Mia says,

“I will pay back the same amount because the average of 1% and 5% is 3%”

Is she correct?
You must show your working.

After 2 years, how much more is investment B worth than investment A?

£........................

Mirek invests £6000 at a compound interest rate of 1.5% per year.

He wants to earn more than £1000 interest.

Work out the least time, in whole years, that this will take.

.......................years

The value of a new car is £18 000
The value of the car decreases by

25% in the first year
12% in each of the next 4 years.

Work out the value of the car after 5 years.

£..........................

Max invests $6000 in a savings account for 3 years.
The account pays compound interest at a rate of 1.5% per year for the first 2 years.

The compound interest rate changes for the third year.
At the end of 3 years, there is a total of $6311.16 in the account.

Work out the compound interest rate for the third year.
Give your answer correct to 1 decimal place.

.....................%

Jan invests  in a savings account.
The account pays compound interest at a rate of  per year.

At the end of  years, there is a total of in the account.

Work out the value of 
Give your answer correct to  decimal places.

............................................... 

Amelia buys a new car.
The expected future value of this car, , is given by

where is the age of the car in complete years.

£ ..................... [1]

 [1]

Show that the expected value of the car when 2 years old is £9000.

Amelia sketches a graph to show the expected value of her car as it gets older.

Explain how you know that Amelia’s graph is incorrect.

Amelia assumes that her car will have no value at all after 20 years.

Explain why her assumption is mathematically incorrect.

On 1st November 2015 there were 4200 trees planted in a wood.
On 1st November 2016, only 3948 of these trees were still alive.

It is assumed that the number of trees still alive is given by

where N  is the number of trees still alive t years after 1st November 2015.

Write down the value of .

Show that r is 0.94.

Show that on 1st November 2030 the number of trees still alive is predicted to have decreased by over 60% compared with 1st November 2015.

Here are the interest rates for two accounts.

Derrick has £10000 he wants to invest.

Calculate which account would give him most money if he invests his money for 3 years.
Give the difference in the interest to the nearest penny.

Account ................... by ................... p 

Explain why he might not want to use Account A.

Naoby invests £6000 for 5 years.
The investment gets compound interest of  per annum.

At the end of 5 years the investment is worth £8029.35

Work out the value of .

Jean invests  in an account paying compound interest for  years.

In the first year the rate of interest is 
At the end of the first year the value of Jean's investment is 

In the second year the rate of interest is 

What is the value of Jean's investment at the end of  years?

Jack bought a new boat for 

The value, , of Jack's boat at the end of years is given by the formula

At the end of how many years was the value of Jack's boat first less than of the value of the boat when it was new?

A savings account pays interest at a rate of  per year.
Jack invests £5500 in the account for one year.

At the end of the year, Jack pays tax on the interest at a rate of 40%.
After paying tax, he gets £79.20

Work out the value of .

Katy invests  in a savings account for  years.

The account pays compound interest at an annual rate of

 for the first year
 for the second year
 for the third year

There is a total amount of  in the savings account at the end of  years.

Work out the rate of interest in the second year.

Katy goes to work by train.

The cost of her weekly train ticket increases by 12.5% to £225

Work out the cost of her weekly train ticket before this increase.

Himari invests 200 000 yen for 3 years in a savings account paying compound interest.
The rate of interest is 1.8% for the first year and for each of the second year and the third year.

The value of the investment at the end of the third year is 209 754 yen.

Work out the value of
Give your answer correct to one decimal place.

...................................................... 

At the start of 2018, the population of a town was 17150.
At the start of 2019, the population of the town was 16807.

It is assumed that the population of the town is given by the formula

where P is the population of the town t years after the start of 2018.

Write down the value of

Show that r = 0 98.

Show that the population is predicted to be less than 16 000 at the start of 2022.

Use the formula to work out what the population might have been at the start of 2017.