Simple and compound interest Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Simple and compound interest questions. See exactly how to solve problems on simple interest, percentage of an amount, one year, I = PRT/100.

simple interestpercentage of an amountone yearI = PRT/100total amountcompound interest
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Ravi invests £2000\pounds 2000 in an account paying 5%5\% simple interest per year. Work out the interest he earns in 11 year.

Worked solution

  1. Write down the simple interest formula

    I=P×R×T100I = \frac{P \times R \times T}{100}

    Simple interest is worked out on the ORIGINAL amount every year, so one formula covers all the years.

  2. Substitute the values

    I=2000×5×1100I = \frac{2000 \times 5 \times 1}{100}

    P=£2000P = \pounds 2000 is the amount invested, R=5R = 5 is the rate and T=1T = 1 is the number of years.

  3. Work out the interest

    I=10000100=£100I = \frac{10000}{100} = \pounds 100

    The interest earned is £100\pounds 100.

Answer
£100\pounds 100
Question 2
1 markeasy
£400\pounds 400 is invested at 3%3\% simple interest per year. Work out the interest earned in 11 year.

Worked solution

  1. Write down the simple interest formula

    I=P×R×T100I = \frac{P \times R \times T}{100}

    Simple interest is worked out on the ORIGINAL amount every year, so one formula covers all the years.

  2. Substitute the values

    I=400×3×1100I = \frac{400 \times 3 \times 1}{100}

    P=£400P = \pounds 400 is the amount invested, R=3R = 3 is the rate and T=1T = 1 is the number of years.

  3. Work out the interest

    I=1200100=£12I = \frac{1200}{100} = \pounds 12

    The interest earned is £12\pounds 12.

Answer
£12\pounds 12
Question 3
2 markseasy
£600\pounds 600 is invested at 4%4\% simple interest per year. Work out the total interest earned in 33 years.

Worked solution

  1. Write down the simple interest formula

    I=P×R×T100I = \frac{P \times R \times T}{100}

    Simple interest is worked out on the ORIGINAL amount every year, so one formula covers all the years.

  2. Substitute the values

    I=600×4×3100I = \frac{600 \times 4 \times 3}{100}

    P=£600P = \pounds 600 is the amount invested, R=4R = 4 is the rate and T=3T = 3 is the number of years.

  3. Work out the interest

    I=7200100=£72I = \frac{7200}{100} = \pounds 72

    The interest earned is £72\pounds 72.

Answer
£72\pounds 72
Question 4
2 markseasy
Nadia invests £1500\pounds 1500 at 2%2\% simple interest per year. Work out the total interest she earns in 22 years.

Worked solution

  1. Write down the simple interest formula

    I=P×R×T100I = \frac{P \times R \times T}{100}

    Simple interest is worked out on the ORIGINAL amount every year, so one formula covers all the years.

  2. Substitute the values

    I=1500×2×2100I = \frac{1500 \times 2 \times 2}{100}

    P=£1500P = \pounds 1500 is the amount invested, R=2R = 2 is the rate and T=2T = 2 is the number of years.

  3. Work out the interest

    I=6000100=£60I = \frac{6000}{100} = \pounds 60

    The interest earned is £60\pounds 60.

Answer
£60\pounds 60
Question 5
2 markseasy
£800\pounds 800 is invested at 5%5\% simple interest per year. Work out the total amount in the account after 11 year.

Worked solution

  1. Work out one year of simple interest

    5%×£800=5100×800=£405\% \times \pounds 800 = \frac{5}{100} \times 800 = \pounds 40

    Simple interest is the same every year because it is always 5%5\% of the original £800\pounds 800.

  2. Multiply by the number of years

    £40×1=£40\pounds 40 \times 1 = \pounds 40

    Over 11 year(s) the total interest is £40\pounds 40.

  3. Add the interest to the amount invested

    £800+£40=£840\pounds 800 + \pounds 40 = \pounds 840

    The account holds £840\pounds 840 in total.

Answer
£840.00\pounds 840.00

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