A-Level Percentage Practice Questions

Q1. £4,000 is invested at 3.5% per annum compounded annually. Calculate the value of the investment after 4 years, giving your answer to the nearest penny.

Q2. £6,500 is placed in a savings account paying 2.8% per annum compounded monthly. Find the value of the account after 3 years, giving your answer to the nearest penny.

Q3. A savings account pays 4.2% per annum compounded quarterly. Calculate the effective annual rate (EAR), giving your answer correct to 3 significant figures.

Q4. Noah invests £10,000 at 5% per annum compounded monthly. Asha invests the same amount at 5% per annum compounded annually. After 5 years, who has more money and by how much? Give your answer to the nearest penny.

Q5. A town has a population of 38,000, growing at 1.8% per year. Estimate the population after 8 years, giving your answer to the nearest hundred.

Q6. An investment grows according to the model V = 2000e^(0.06t), where V is the value in pounds and t is the time in years. Find the value after 7 years and the percentage increase over this period, both to 3 significant figures.

Q7. A country's GDP index was 100 in 2010 and grew at a constant annual rate. By 2018 the index had reached 134.7. Find the annual percentage growth rate correct to 3 significant figures. Hence estimate the index value in 2022.

Q8. A radioactive substance has an initial mass of 200 g and decays at 8% per year. Find the mass remaining after 10 years, giving your answer to 3 significant figures.

Q9. A car is purchased for £18,500 and depreciates at 14% per year. After how many complete years will it first be worth less than £8,000? Show your working clearly.

Q10. A drug is administered to a patient. The concentration C mg/L at time t hours is modelled by C = 12e^(-0.25t). Find: (a) the initial concentration, (b) the concentration after 4 hours, (c) the time at which the concentration falls below 1 mg/L.

Q11. £5,000 is invested at 4% per annum continuously compounded. Calculate the value after 8 years, giving your answer to the nearest penny.

Q12. £12,000 is invested for 6 years. Account A pays 3.5% per annum compounded monthly. Account B pays 3.45% per annum continuously compounded. Which account gives the greater return and by how much? Give your answer to the nearest penny.

Q13. A population is modelled by P = 4000e^(0.025t), where t is the time in years. State the annual percentage growth rate. Find dP/dt and use it to verify the relative rate of change.

Q14. The value V of a vintage wine collection grows according to V = V₀e^(kt). After 3 years, V = 1.2V₀. Find k and the annual percentage rate of growth, giving your answer to 3 significant figures.

Q15. The number of bacteria N satisfies dN/dt = 0.05N, with N(0) = 800. (a) Write N as a function of t. (b) Find N when t = 10. (c) Find the time at which N = 5,000, giving your answer to 3 significant figures.

Q16. The UK RPI index was 279.9 in January 2020 and 296.4 in January 2022. Calculate the percentage increase in the RPI over this period, giving your answer to 3 significant figures.

Q17. A company's output index was 100 in 2015. The index was 112 in 2017 and 131.6 in 2023. Calculate (a) the percentage increase in output from 2015 to 2023, and (b) the percentage increase from 2017 to 2023.

Q18. In 2010, the average price of a house was £180,000. The house price index (base 2010 = 100) was 145.9 in 2018 and 162.4 in 2022. Calculate the average house price in 2022. Verify that prices rose by 11.3% between 2018 and 2022.

Q19. The UK CPI index (base 2015 = 100) grew continuously at 3.1% per year from 2015. (a) Write a model C(t) = 100e^(rt) and state r. (b) Find the predicted index in 2023 (t = 8). (c) Given the actual index was 128.4 in 2023, compare with your prediction. (d) Find the year in which the model first predicts an index of 150.

Q20. A chemical compound decomposes in solution. Its concentration C mmol/L at time t minutes satisfies C = C₀e^(-kt). Initially C₀ = 50 mmol/L and after 15 minutes the concentration is 35 mmol/L. (a) Find k to 3 s.f. (b) Find the concentration after 30 minutes. (c) Find dC/dt and evaluate the rate of decrease at t = 10 minutes. (d) Find the half-life.