Repeated percentage change and compound interest

Hollie puts £8000 into a savings account.

The value of the account increases by 5% each year.

Work out the value of the account after 2 years.

Rosa puts £3000 into a savings account.

The account pays 2% compound interest per year.

Work out the value of her savings at the end of 2 years.

Dev buys a van for £15 000.

The value of the van depreciates by 12% each year.

Calculate the value of the van at the end of 3 years.

Give your answer to the nearest penny.

Ben buys a car for £16 000.

The value of the car depreciates by 15% each year.

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

The number of visitors to a website increases by 50% one month and then increases by 50% again the next month.

Petra says, "Two increases of 50% make an increase of 100%."

Petra is wrong.

Find the overall percentage increase over the two months.

Zainab invests £2500 in an account paying 3% compound interest per year.

Work out the total interest she earns in 3 years. Give your answer to the nearest penny.

Zara invests £2500 in a savings account paying 3% compound interest per year.
Work out the total amount in the account after 4 years.

The population of a colony of seabirds falls by the same percentage each year.

Three years ago the population was 64 000.

The population is now 46 656.

Find the annual percentage decrease.

Theo puts £4000 into a savings account for 2 years.

The account pays 4% compound interest in the first year and 2% compound interest in the second year.

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

Oliver invests £4000 for 3 years at 2.5% per year.

1. Work out the total interest if it is simple interest.
2. Work out the total interest if it is compound interest.
3. How much more interest is earned with compound interest?

Ellis invests £4000 in a savings account for 3 years.

The account pays compound interest at an annual rate of

3% for the first year

2.5% for each of the second and third years.

Work out the value of the investment at the end of 3 years.

Give your answer to the nearest penny.

A delivery van is bought for £24 500.

Its value depreciates by 18% each year.

Work out the value of the van at the end of 3 years. Give your answer to the nearest pound.

Mia invested some money for 2 years at 4% compound interest per year. After 2 years she had £2163.20 in the account.

1. Work out how much she invested.
2. Mia's brother invests the same amount for 3 years at 3.5% compound interest per year. Who has more money in the account at the end of their investment, and by how much?

Sasha has £6000 to invest for 4 years.
Account A pays 2.5% compound interest per year.
Account B pays 2.6% simple interest per year.
Which account gives more interest after 4 years, and by how much?

At the start of an experiment there are 20 000 bacteria in a dish.

The number of bacteria increases by 8% each hour.

A scientist claims there will be more than 25 000 bacteria after 3 hours.

Work out whether the scientist is correct.

You must show your working.

Freya buys a motorbike for £7200.

Its value depreciates by 12% each year.

Show that the value of the motorbike at the end of 3 years is less than £5000.

A running club has 800 members.

The number of members increases by 15% each year.

Find the number of complete years it takes for the number of members to first exceed 1600.

Idris puts £5000 into an account for 2 years.

The account pays 3% compound interest in the first year and r% compound interest in the second year.

At the end of 2 years the account is worth £5253.

Work out the value of r.

The population of a town is growing by 12% each year.

Find the number of complete years it will take for the population to become more than double its current size.

Meg has £2000 to invest for 3 years. She can choose one of two accounts.

Account A pays 2.5% compound interest every year.

Account B pays 3% compound interest in the first year, then 2.2% compound interest in each of the next 2 years.

Work out which account gives Meg more money at the end of 3 years, and by how much.

Town A has a population of 150 000. Its population is falling by 4% each year.

Town B has a population of 120 000. Its population is rising by 5% each year.

Work out which town will have the larger population at the end of 3 years.

You must show your working.

Ava invests £6000 at a rate of x% compound interest per year.

At the end of 2 years the investment is worth £6615.

Work out the value of x.

The value of a painting increased by 10% each year for two years.

The painting is now worth £9680.

Find the value of the painting two years ago.

Tomasz puts £8000 into an account paying 4% compound interest per year.

At the end of the first year, after the interest has been added, he withdraws £1500.

He leaves the rest in the account for another year.

Work out how much is in the account at the end of the second year.

Nina has £10 000 to invest for 3 years. She can choose one of two accounts.

Steady Saver pays 2.1% compound interest every year.

Flex Saver pays 3.5% compound interest in the first year, then 1.5% compound interest in each of the next 2 years.

Which account should Nina choose to get the most money after 3 years? You must show how much more it pays.

Kira invests £8000 in an account paying 5% compound interest per year.

At the end of 2 years she uses all the money in the account to buy a car.

The value of the car depreciates by d% each year.

Exactly 2 years after she buys it, the car is worth £5644.80.

Work out the value of d.