A-Level Percentage Worksheet

£3,000 is invested at 4% per annum compounded annually. Calculate the value of the investment after 5 years, giving your answer to the nearest penny.

£7,500 is invested at 3.6% per annum compounded monthly. Find the value of the account after 4 years, giving your answer to the nearest penny.

A bank offers 5.4% per annum compounded quarterly. Calculate the effective annual rate (EAR), giving your answer correct to 3 significant figures.

£2,000 is invested at 4.5% per annum compound interest. After how many complete years will the investment first exceed £2,750? Show your working clearly.

A city has a population of 250,000, growing at 2.1% per year. Estimate the population after 10 years, giving your answer to the nearest thousand.

A town's population grew from 42,000 to 50,820 over 6 years. Assuming exponential growth, find the annual percentage growth rate correct to 3 significant figures.

An investment grows according to V = 5000e^(0.045t), where t is in years. Find the value after 12 years and the percentage increase over this period, both to 3 significant figures.

A radioactive substance has an initial mass of 500 g and decays at 6% per year. Find the mass after 15 years, giving your answer to 3 significant figures.

A radioactive isotope decays at 5.5% per year. Find its half-life, giving your answer to 3 significant figures.

A van is purchased for £24,000 and depreciates at 16% per year. Find its value after 5 years and the percentage of the original value remaining, both to 3 significant figures.

£9,000 is invested at 3.8% per annum continuously compounded. Calculate the value after 6 years, giving your answer to the nearest penny.

Account A pays 4.2% per annum compounded monthly. Account B pays 4.15% per annum continuously compounded. For an investment of £15,000 over 5 years, which account is more profitable? Give your answer to the nearest penny.

A population P is modelled by P = 3000e^(0.035t). Write down the annual percentage growth rate and verify it using differentiation.

A quantity Q satisfies dQ/dt = 0.08Q with Q(0) = 600. Write Q as a function of t. Find Q when t = 5. Find the time at which Q = 1,200, giving your answer to 3 significant figures.

An exponential model N = N₀e^(kt) describes a bacteria colony. After 5 hours, the colony is 1.4 times its original size. Find k to 3 significant figures and state the percentage growth rate per hour.

The UK CPI index was 100 in 2015. In 2020 the index was 108.9 and in 2023 it was 128.4. Calculate the percentage increase in prices from 2015 to 2020 and from 2020 to 2023.

A basket of goods cost £240 in 2010 (base year, index = 100). The price index stood at 141.6 in 2022. Calculate the cost of the same basket in 2022.

A company's electricity costs were £12,000 in 2018, £13,440 in 2019, £14,784 in 2020 and £18,048 in 2022. Construct an index with 2018 as the base year and calculate the percentage increase in electricity costs from 2019 to 2022.

A country's GDP index (base 2010 = 100) grew at a continuous rate of 2.4% per year from 2010. (a) Write a model G(t) = 100e^(rt) and state r. (b) Find the predicted index in 2020. (c) The actual index in 2020 was 127.6. Find the actual average annual compound growth rate, correct to 3 s.f. (d) In which year does the continuous model first predict an index of 175?

A medicine is administered and its concentration C mg/L in the blood satisfies C = 40e^(-0.12t), where t is in hours. (a) State the initial concentration. (b) Find C after 6 hours. (c) Find dC/dt and interpret its value at t = 0. (d) Find the half-life. (e) After how many complete hours is C first below 5 mg/L?