Simple & Compound Interest, Growth & Decay (Cambridge (CIE) IGCSE Maths: Extended)

Hong has $4000 to invest.
She invests $2000 at a rate of 2.5% per year simple interest.
She also invests $2000 at a rate of 2% per year compound interest.

i)  Find the value of each investment at the end of 8 years.

Simple interest investment $ .................................................... Compound interest investment $ ................................................[5]

ii)  Find the overall percentage increase in the $4000 investment at the end of 8 years.

............................................% [2]

Find the number of complete years it takes for the compound interest investment of $2000 to become greater than $2500.

[3]

Beth invests $2000 at a rate of 2% per year compound interest.

i) Calculate the value of this investment at the end of 5 years.

     $ ................................................ [2]

ii) Calculate the overall percentage increase in the value of Beth’s investment at the end of 5 years.  

............................................. % [2]

iii) Calculate the minimum number of complete years it takes for the value of Beth’s investment to increase from $2000 to more than $2500. 

 [3]

Ollie invests $200 at a rate of 0.0035% per day compound interest.  

Calculate the value of Ollie’s investment at the end of 1 year. [1 year = 365 days.]  

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

The value of a gold ring increases exponentially at a rate of 5% per year. The value is now $882.

i) Calculate the value of the ring 2 years ago.

$ ................................................... [2]

ii) Find the number of complete years it takes for the ring’s value of $882 to increase to a value greater than $1100.

[2]

Mohsin’s earnings increase exponentially at a rate of 8.7% each year.
During 2018 he earned $195 600.

During 2027, how much more does he earn than during 2018?

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

Bryan invested $480 in an account 4 years ago.
The account pays compound interest at a rate of 2.1% per year. Today, he uses some of the money in this account to buy a bicycle costing $430.

Calculate how much money remains in his account.

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

In a city the population is increasing exponentially at a rate of 1.6% per year.  
Find the overall percentage increase at the end of 20 years.  

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

Alain invests $5000 at a rate of % per year compound interest. At the end of 15 years, the value of the investment is $7566.

Find the value of .

 = ..............................................

Paddy and Anna each invest $2000 for 5 years.
Paddy earns simple interest at a rate of 1.25% per year.
Anna earns compound interest at a rate of % per year.
At the end of 5 years, Paddy’s investment is worth the same as Anna’s investment.  

Calculate the value of .  

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

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

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

Work out the value of x.

Jack bought a new boat for £12 500

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

At the end of how many years was the value of Jack's boat first less than 50% of the value of the boat when it was new?

A savings account pays interest at a rate of R% 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 R.

Jean invests £12000 in an account paying compound interest for 2 years.

In the first year the rate of interest is %
At the end of the first year the value of Jean's investment is £12336

In the second year the rate of interest is %

What is the value of Jean's investment at the end of 2 years?

Katy invests £2000 in a savings account for 3 years.

The account pays compound interest at an annual rate of

2.5% for the first year

x% for the second year

x% for the third year

There is a total amount of £2124.46 in the savings account at the end of 3 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.

Alan invests $200 at a rate of  per year compound interest.
After 2 years the value of his investment is $206.46.  

Show that     .

The population of a village decreases exponentially at a rate of 4% each year.
The population is now 255.

Calculate the population 16 years ago.

The population of the Earth in 2017 was estimated to be 7.53 × 10⁹.
The population of the Earth in 2000 was estimated to be 6.02 × 10⁹.
Assume that the population of the Earth increased exponentially by % each year for these 17 years.  

Find the value of .  

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

Edna invests $500 at a rate of % per year compound interest. At the end of 6 years, the value of Edna’s investment is $559.78.  

Find the value of .  

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

The value of the campsite has increased exponentially by 1.5% every year since it opened 30 years ago. 

Calculate the value of the campsite now as a percentage of its value 30 years ago.  

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

The value of Dhanu’s model railway is $550.
This value increases exponentially at a rate of % per year.
At the end of 5 years the value will be $736.

Calculate the value of .

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

Hans invests $550 at a rate of % per year compound interest. At the end of 10 years, the value of the investment is $638.30, correct to the nearest cent.

Find the value of

= ..............................................

The population of a village is 6400.
The population is decreasing exponentially at a rate of  per year.
After 22 years, the population will be 2607.  

Find the value of .  

= ....................................................

The number of a particular newspaper sold decreases exponentially by each year.
Over a period of 21 years the number of newspapers sold decreases from to .

Calculate the value of .   

= ..............................................

A bacteria population increases exponentially at a rate of % each day.
After 32 days, the population has increased by 309%.

Find the value of .  

= .................................................

Over a period of 3 years, a company’s sales of biscuits increased from 15.6 million packets to 20.8 million packets.
The sales increased exponentially by the same percentage each year.

Calculate the percentage increase each year.

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

Tomas has two cars.

i) The value, today, of one car is $21 000.
The value of this car decreases exponentially by 18% each year.

Calculate the value of this car after 5 years. Give your answer correct to the nearest hundred dollars.

$ ............................................... [3]

ii) The value, today, of the other car is $15 000.
The value of this car increases exponentially by % each year. After 12 years the value of the car will be $42 190.

Calculate the value of .

............................................... [3]