Test 2. Compound interest-type problems

 1. A new car is bought for £23000. Each year, its value depreciates (goes down) by 15% of its value at the start of the year. How much is the car worth after 3 years?  

 а) £14,125.18 ;     

 b)  £14,124.60;     

 c)  £14,126.68;     

 d)  £14,124.88.

 2. The population of a country decreases by 4% of its size at the start of every year. If the population is 8 million, what will it be after 3 year?

 а)  7,077.888;     

 b)  7,077.868;     

 c)  7,078.866;     

 d)  7,074.634.

 3. A bacteria culture starts with 4000 bacteria. Each hour the number of bacteria increases by 20%. How many bacteria will there be after 3 hours?

 а)  6914;      b)  6922;     

 c)  6912;      d)  6916.

 4. Mohammed puts £200 in a bank at 6% p. a. (per annum) compound interest. Geena puts £210 in a bank at 4% p. a. compound interest. What will have more money in the bank after 2 years?

 а)  ;      b)  Geena;     

 c)  ;      d)  Mohammed.

 5. Mohammed puts £200 in a bank at 6% p. a. (per annum) compound interest. Geena puts £210 in a bank at 4% p. a. compound interest. How much more?

 а)  £2.46;      b)  £2.84;     

 c)  £2.42;      d)  £2.22.

 6. £800 is put in a bank with 10% p. a. (per annum) compound interest. Work out the total money in the bank after 3 years (use percentage multiplier 1.1).

 а)  £1064.80;     

 b)  £1068.80;     

 c)  £1065.45;     

 d)  £1064.60.

 7. £800 is put in a bank with 10% p. a. (per annum) compound interest. How much money is in the bank after 5 years?

 а)  £1288.53;     

 b)  £1288.41;     

 c)  £1286.45;     

 d)  £1289.49.

 8. £800 is put in a bank with 10% p. a. (per annum) compound interest. How much money is in the bank after 10 years? (just multiply £800 by 1.1 ten times)

 а)  £2074.99;     

 b)  £2076.89;     

 c)  £2074.66;     

 d)  £2075.50.

 9. Another bank pays 7% p. a. compound interest. If you put in £400, how much money would be in the bank after 2 years?

 а)  £457.96;     

 b)  £457.96;     

 c)  £457.96;     

 d)  £457.96.

10. Another bank pays 7% p. a. compound interest. If you put in £400, how much money would be in the bank after 3 years?

 а)  £490.02;      b)  £494.02;     

 c)  £492.20;      d)  £490.12.

11. Another bank pays 7% p. a. compound interest. If you put in £400, how much money would be in the bank after 5 years?

 а)  £560.20;      b)  £562.12;     

 c)  £561.02;      d)  £561.24.

12. A building society offers 4.7% p. a. compound interest. If you put £1200 into the building society, how much would you have 3 years later?

 а)  £1378.44;     

 b)  £1376.20;     

 c)  £1377.48;     

 d)  £1377.28.

Test 1. Compound interest-type problems

 1. £5000 is invested at 10% per annum (year) compound interest. How much money will there be after 2 years?

 а)  £6050;      b)  £6070;     

 c)  £6120;      d)  £6055.

 2. Ben invests £6000 in bank at 5% per annum compound interest. How much money will he have in the bank after 2 years?

 а)  £6625;      b)  £6615;     

 c)  £6515;      d)  £6660.

 3. A bank pays 6% per annum compound interest. How much will the following people have in the bank after the number of years stated?

Kim: £9000 after 2 years.

 а)  £10,714.16;     

 b)  £10,714.10;     

 c)  £10,718.14;     

 d)  £10,714.14.

 4. A bank pays 6% per annum compound interest. How much will the following people have in the bank after the number of years stated?

Freddie: £4000 after 3 years.

 а) £4766.66 ;     

 b)  £4764.60;     

 c)  £4764.06;     

 d)  £4764.08.

 5. A bank pays 6% per annum compound interest. How much will the following people have in the bank after the number of years stated?

Les: £2500 after 2 years.

 а)  £2819;      b)  £2809;     

 c)  £2812;      d)  £2803.

 6. A bank pays 6% per annum compound interest. How much will the following people have in the bank after the number of years stated?

Olive: £600 after 2 years.

 а)  £674.16;     

 b)  £676.18;     

 c)  £672.12;     

 d)  £664.96.

 7. A stereo loses 30% of its value every year. Tim bought it for £800. How much would it be worth after 2 years?

 а)  £398;      b)  £382;     

 c)  £392;      d)  £390.

 8. A stereo loses 30% of its value every year. Tim bought it for £800. How much would it be worth after 3 years?

 а)  £274.40;      b)  £274.60;     

 c)  £278.45;      d)  £276.60.

 9. The number of fish in a lake is decreasing by 5% each year. There are 10000 fish in the lake at the start of 2005. How many fish are there in the lake at the end of 2005?

 а)  9520;      b)  9500;     

 c)  9480;      d)  9550.

10. The number of fish in a lake is decreasing by 5% each year. There are 10000 fish in the lake at the start of 2005. How many fish are there in the lake at the end of 2006?

 а)  9015;      b)  9020;     

 c)  9025;      d)  9055.

11. Inflation is how much more expensive things in the shop get each year. Inflation is about 3%. If a pair of shoes costs £50, how much will the pair of shoes cost after 2 years?

 а)  £52.05;      b)  £53.20;     

 c)  £53.15;      d)  £53.05.

12. Inflation is how much more expensive things in the shop get each year. Inflation is about 3%. If a pair of shoes costs £50, how much will the pair of shoes cost after 3 years?

 а)  £54.44;      b)  £54.64;     

 c)  £54.68;      d)  £54.60.

Lesson 10. Compound interest-type problems

EXSAMPL:

Suppose £2000 is invested at 10% per annum (year) compound interests. How much money will there be after 2 years?

‘compound’ interest here means that the interest must be worked out separately for each year.

After 1 year:

Do a new calculation for the interest in the second year.

After 2 year:

EXSAMPL:

A car is bought for £12000. Each year, its value depreciates (goes down) by 5% of its value at the start of the year. How much is the car worth after 2 year?

After 1 year:

loss = 5% of 12000 = 600

value of car = 12000 – 600

= 11400

After 2 year:

loss = 5% of 11400 = 570

value of car = 11400 – 570

= £10830

Simple interest.

This means work out the interest for one year then multiply by the number of year.

EXSAMPL:

£2000 is invested at 10% per annum (year) simple interests. How much money will there be after 2 years?

Using percentage multipliers.

EXSAMPL:

£500 is invested in a bank at 14% per annum compound interest. How much money is in the bank after 5 years?

Use a percentage multiplier

1.14(100% + 14% = 114%)

Now multiply by 1.14 every year to get the new amount.

Start with £500:

after 1 year:

500 × 1.14 = 570

after 2 year:

570 × 1.14 = 649.80

and soon

after 5 year:

total money =

= 962.70729…

= 962.71 (to the nearest penny) 

Tasks to the lesson 10

• Test 1
• Test 2
• Test 3

Other lessons:

• Lesson 1. Patio
• Lesson 3. Direct proportion
• Lesson 5. Sharing in a given ratio
• Lesson 6. Percentages
• Lesson 7. Percentage of a number
• Lesson 9. Percentage change
• Lesson 11. Tasks for a time