Simple and compound interest

Ratio, proportion and rates of change

Questions marked Higher are aimed at the Higher tier.

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Find the simple interest on £$400$ at $5\%$ per year for $3$ years, and the total amount.

2 marks
Find the simple interest on £$200$ at $3\%$ per year for $4$ years.

2 marks
£$400$ is invested at $5\%$ compound interest for $2$ years. Find the interest.

3 marks
Find the amount when £$1000$ is invested at $4\%$ simple interest for $3$ years.

3 marks
£$2500$ is invested at $3\%$ compound interest for $3$ years. Find the amount to the nearest penny.

4 marks
Maya invests £$800$ at $2.5\%$ simple interest. For how many years must it be invested for the interest to be £$100$?

4 marks
£$1500$ is invested at $4\%$ for $2$ years. Find the compound amount, the compound interest, and how much more this is than simple interest at the same rate. Higher

5 marks
Jo invests £$2000$. Option A pays $3\%$ simple interest for $4$ years. Option B pays $2.8\%$ compound interest for $4$ years. Find both amounts to the nearest penny, and say which option gives more. Higher

6 marks

Mark scheme

Answer. Interest £$60$, total £$460$
- $400 \times 0.05 \times 3 = 60$
- Total $= 460$
Answer. £$24$
- $200 \times 0.03 \times 4$
- £$24$
Answer. £$41$
- $400 \times 1.05^{2} = 441$
- Interest $= 441 - 400 = 41$
Answer. £$1120$
- Interest $= 1000 \times 0.04 \times 3 = 120$
- Amount $= 1120$
Answer. £$2731.82$
- $1.03^{3} = 1.092727$
- $2500 \times 1.092727 = 2731.8175$
- £$2731.82$
Answer. $5$ years
- Interest per year $= 800 \times 0.025 = 20$
- $100 \div 20 = 5$ years
Answer. Amount £$1622.40$, interest £$122.40$, which is £$2.40$ more than simple interest
- $1500 \times 1.04^{2} = 1622.40$
- Compound interest $= 122.40$
- Simple interest $= 1500 \times 0.04 \times 2 = 120$, so the difference is £$2.40$.
Answer. A gives £$2240$ and B gives £$2233.58$. Simple interest gives £$6.42$ more.
- Simple interest $= 2000 \times 0.03 \times 4 = 240$, so the amount is £$2240$.
- $1.028^{4} = 1.116792\ldots$
- $2000 \times 1.116792 = 2233.58$ to the nearest penny.
- Option A gives £$6.42$ more.