Simple Interest (Cambridge International IGCSE Mathematics)

Simple Interest

What is simple interest?

• Interest is money that is regularly added to an original amount of money

  • This could be added yearly, monthly, etc
  • When saving money, interest helps increase the amount saved
  • With debt, interest increases the amount owed

• Simple interest refers to interest which is based only on the starting amount

  • Each interest payment (or charge in the case of debt) will be the same

How do I calculate simple interest?

• To find the total simple interest earned

  • Find a percentage(the percentage rate) of the starting amount

    • Use a multiplier to do this (e.g. 0.05 to find 5%)

  • Multiply this by the number of time periods (e.g. years) it is being applied for

• To find the total balance after the simple interest has been earned

  • Use the same method as above, and add this on to the starting amount

Exam Hint

• Double check:

  • Does the question ask for the interest earned, or the total amount at the end?
  • Do you need to round your answer? (e.g. to the nearest hundred)

Worked Example A bank account offers simple interest of 4% per year. Nigel puts $ 250 into this bank account, and leaves it to earn interest for 6 years.

(a) Find the total amount of interest earned over the 6 year period.

Answer:

Each year, 4% of the starting amount is added as interest Find 4% of $ 250 using a multiplier

0.04 × 250 = 10

This amount of interest is earned every year, for 6 years

10 × 6 = 60

$ 60 of interest is earned

(b) Find the total amount in the bank account at the end of the 6 year period.

Answer:

Add the amount of interest earned, found in part (a), to the starting amount

250 + 60 = 310

Final answer: $ 310

Worked Example Noah invests £ 9000 at a rate of $n \%$ simple interest per year, for 5 years. At the end of 5 years there is £ 11 700 in the account. Find the value of $n$.

Answer:

Find the total amount of interest earned over the 5 years

11 700 - 9 000 = £ 2 700 total interest

As we are dealing with simple interest, the same amount of interest is earned each year Find the interest earned each year

2 700 ÷ 5 = £ 540 interest per year

Find what percentage of the original amount this represents

$540 / 9000=0.06=6 \%$

£ 540 is 6% of the original £ 9000

$n=6$