Simple & Compound Interest, Growth & Decay

Liam invests £6200 for 3 years in a savings account.
He gets 2.5% per annum compound interest.

How much money will Liam have in his savings account at the end of 3 years?

Peter has £20 000 to invest in a savings account for 2 years.

He finds information about two savings accounts.

Peter wants to have as much money as possible in his savings account at the end of 2 years.

Which of these savings accounts should he choose?

This notice was in a car magazine.

Paul bought a new car.
The value of the car was £15 000

In the first year, the value of the car depreciated by 23%.
After the first year, the value of the car depreciated by 18% each year.

Work out if Paul's car lost more than half of its value by the end of three years.

Derek buys a house for £150 000
He sells the house for £154 500

Work out Derek's percentage profit.

Derek invests £154 500 for 2 years at 4% per year compound interest.

Work out the value of the investment at the end of 2 years.

Anil wants to invest £25 000 for 3 years in a bank.

Which bank will give Anil the most interest at the end of 3 years?

You must show all your working.

A virus on a computer is causing errors.
An antivirus program is run to remove these errors.

An estimate for the number of errors at the end of hours is 

Work out an estimate for the number of errors on the computer at the end of hours.

Explain whether the number of errors on this computer ever reaches zero.

Katy invests £200 000 in a savings account for 4 years.
The account pays compound interest at a rate of 1.5 % per annum.

Calculate the total amount of interest Katy will get at the end of 4 years.

Zhi bought a house on 1st January 2017
When she bought the house, its value was 120 000 yuan.

The value of the house increased by 1.8% per year.

Work out the value of Zhi’s house on 1st January 2020
Give your answer correct to 3 significant figures.

....................................................... yuan

Ali and Badia each have 25000 dollars to invest.

Ali invests in the Cyclone Bank for 3 years.
Badia invests in the Tornado Bank for 3 years.

By the end of the 3 years, Ali will have received more interest than Badia.

How much more?
Show your working clearly.
Give your answer correct to the nearest dollar.

....................................................... dollars

Hamish buys a new car for $20 000
The car depreciates in value by 19% each year.

Work out the value of the car at the end of 3 years.
Give your answer to the nearest $.

$ .....................

The price, £P, of a car is £20 000 in 2019.
The price is expected to decrease by 5% each year after 2019.

Jasmine says

This means the price in 2021 is expected to be £18 000.

She is incorrect.
Explain her error and work out the correct answer.

Her error is .........................................................

The correct answer is £ ........................................................... 

Write a formula for in terms of , where is the number of years after 2019.

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

Circle the graph that best represents the price, £, of the car years after 2019.

The value of a house, £H, is given by the formula

H = 165 000 × 1.03^t

where t is the number of years after 1st January 2010.

Write down the value of the house on 1st January 2010.

£ ........................................................

Write down the annual percentage increase in the value of the house.

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

Show that the value of the house is over £200000 on 1st January 2017.

Kay invests £1500 in an account paying 3% compound interest per year.
Neil invests £1500 in an account paying r% simple interest per year.

At the end of the 5th year, Kay and Neil’s accounts both contain the same amount of money.

Calculate r.
Give your answer correct to 1 decimal place.

r = .....................................................

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.