What is Simple Interest?

Simple interest is a way to calculate how much money you earn or owe over time when you borrow or lend money. It is called “simple” because the interest is calculated only on the original amount of money, called the principal.

Key Formula

To find the simple interest (SI), we use the formula:

$$\text{SI} = P \times r \times t$$

Where:

  • SI is the simple interest.
  • P is the principal amount (the original amount of money).
  • r is the rate of interest per year (in decimal form).
  • t is the time in years.

Example

Let’s say you have £100 (this is your principal, P) and the interest rate is 5% per year (this is your r). If you keep the money for 2 years (this is your t), the calculation would look like this:

  1. Convert the interest rate to decimal:$$r = \frac{5}{100} = 0.05$$
  2. Plug the values into the formula:$$\text{SI} = 100 \times 0.05 \times 2$$
  3. Calculate:$$\text{SI} = 100 \times 0.1 = 10$$

So, the simple interest earned after 2 years would be £10.

Key Rules

  1. Interest is always calculated on the principal: The interest does not change even if you earn interest on the interest in other types of interest calculations.
  2. Time must be in years: If the time is given in months, convert it to years by dividing by 12. For example, 6 months would be 0.5 years.
  3. Interest rates should be in decimal: Always convert the percentage to a decimal by dividing by 100.

Tips and Tricks

  • Use a calculator: To help with calculations, especially when dealing with larger numbers.
  • Practice with different rates and time periods: This will help you become more comfortable with the concept.
  • Draw it out: Sometimes, visualising the money growing over time can help you understand it better.

Questions on Simple Interest

Easy Level Questions

  1. What is the principal if you earn £5 in interest at a rate of 5% over 2 years?
  2. If you have £200 and the interest rate is 10% per year, how much interest will you earn in 1 year?
  3. Calculate the simple interest on £150 at a rate of 4% for 3 years.
  4. What is the simple interest on £1000 at 2% for 5 years?
  5. If you lend £50 at an interest rate of 1% for 4 years, how much interest will you earn?
  6. How much will you earn in interest if you invest £300 at 3% for 2 years?
  7. If you have a principal of £400 and earn £8 in interest, what is the rate if it was for 1 year?
  8. What is the total amount after earning £10 interest on £200 for 1 year at 5%?
  9. How much simple interest do you earn on £600 at a rate of 6% over 2 years?
  10. If the interest earned is £12 after 3 years on £400, what was the interest rate?

Medium Level Questions

  1. Calculate the total amount after earning simple interest of £30 on £500 for 2 years at a certain interest rate.
  2. If you borrow £800 at a rate of 5% for 4 years, how much interest will you pay?
  3. What is the principal if you earn £20 in interest at 10% over 2 years?
  4. If you have £250 and earn £5 in interest over 1 year, what is the interest rate?
  5. Calculate the simple interest on £350 at a rate of 7% for 3 years.
  6. What total amount will you have after 5 years if you invest £1,000 at a rate of 4%?
  7. If you receive £15 in interest on £300 in 3 years, what is the interest rate?
  8. Calculate how long it takes to earn £50 in interest on a principal of £1,000 at 5%.
  9. What is the simple interest on £800 at a rate of 3.5% for 2 years?
  10. If you invested £600 and earned £36 in interest, what was the interest rate and for how long?

Hard Level Questions

  1. If you need to have £1,500 after 5 years, how much should you invest now at an interest rate of 4%?
  2. Calculate the time needed to earn £200 in interest on £2,000 at a rate of 5%.
  3. What is the principal if the simple interest earned is £100 at a 2% rate over 5 years?
  4. If a loan of £1,200 has a total repayment amount of £1,500 after 2 years, what was the interest rate?
  5. How much interest would you earn on £750 at a rate of 6% after 4 years?
  6. If you invest £900 and the total amount after 3 years is £1,080, what was the interest rate?
  7. How long would it take to earn £90 on a principal of £1,500 at a rate of 6%?
  8. If you invest £1,000 at 8% and receive £240 in interest, how long did you invest it for?
  9. Calculate the principal if the interest earned is £50 in 2 years at a rate of 5%.
  10. What is the total amount you will receive if you invest £400 at an interest rate of 10% for 4 years?

Answers and Explanations

Easy Level Answers

  1. The principal is £50. You can find it by rearranging the simple interest formula. Using the formula, £5 = P × 0.05 × 2, gives P = £50.
  2. You will earn £20 in interest. Using the formula, SI = 200 × 0.1 × 1, gives you £20. Always remember to convert the percentage to a decimal.
  3. The simple interest is £18. Using SI = 150 × 0.04 × 3, we calculate the interest. This shows how much you earn over the time period.
  4. The simple interest is £100. SI = 1000 × 0.02 × 5 gives us this amount. It helps to see how interest grows over years.
  5. You will earn £2 in interest. SI = 50 × 0.01 × 4 equals £2. Every little bit of interest counts!
  6. You will earn £18 in interest. SI = 300 × 0.03 × 2 gives £18. It’s important to keep track of your earnings!
  7. The rate is 4%. Rearranging SI = P × r × t leads to r = 8/200 = 0.04. Always check your calculations!
  8. The total amount is £210. You earned £10 in interest, so you add it to the principal. This shows how your money grows.
  9. The simple interest is £72. Using SI = 600 × 0.06 × 2, we find this amount. It’s useful to see how interest can accumulate.
  10. The interest rate is 10%. Using SI = 400 × r × 3 gives £12, so r = 0.1. This helps you understand interest rates better.

Medium Level Answers

  1. The total amount is £530. You earned £30 on £500 over 2 years. This shows the importance of saving!
  2. You will pay £160 in interest. Using SI = 800 × 0.05 × 4 gives this amount. It’s important to understand borrowing costs.
  3. The principal is £200. SI = 20 = P × 0.1 × 2 gives P = £200. Understanding principal helps in financial decisions.
  4. The interest rate is 2%. Rearranging the formula gives r = 5/250 = 0.02. Knowing rates helps you choose good deals.
  5. The simple interest is £73.50. Using SI = 350 × 0.07 × 3 gives this amount. This shows how interest can add up over time.
  6. You will have £1,200 after 5 years. This includes the interest earned at 4%. It’s great to see your investments grow!
  7. The interest rate is 1.67%. SI = 15 = 300 × r × 3 gives r = 0.0167. It’s very useful to know your earnings rates.
  8. It takes 4 years to earn £50. Using SI = 2000 × 0.05 × t leads to t = 5. Time is money in finance!
  9. The simple interest is £48. SI = 800 × 0.035 × 2 gives this amount. Interest can really benefit savings!
  10. The principal is £600. SI = 36 = P × 0.06 × 2 gives P = £600. Understanding principals helps in financial planning.

Hard Level Answers

  1. You should invest £1,087.08. Using the formula, P = 1500 / (1 + 0.04 × 5) gives this amount. It’s important to invest wisely.
  2. It takes 2 years to earn £200. Using SI = 2000 × 0.05 × t leads to t = 2. Planning your finances is crucial!
  3. The principal is £2,500. SI = 100 = P × 0.02 × 5 gives P = £2,500. Knowing your principal helps in budgeting.
  4. The interest rate is 12.5%. Using SI = 300 = 1200 × r × 2 gives r = 0.125. Understanding loans is key to financial literacy.
  5. You would earn £180 in interest. SI = 750 × 0.06 × 4 gives this amount. It’s important to know your earnings!
  6. The interest rate is 8%. Using SI = 1,080 – 900 = 180, and SI = 900 × r × 3 gives r = 0.08. Good investments grow your money!
  7. It takes 8 years to earn £90. Using SI = 1500 × 0.06 × t leads to t = 1. This shows the long-term benefits of saving!
  8. You invested for 8 years. Using SI = 240 = 1000 × 0.08 × t gives t = 3. Time can really help your money grow!
  9. The principal is £500. SI = 50 = P × 0.05 × 2 gives P = £500. Understanding the principal is essential for managing money.
  10. The total amount is £480. You earned £80 in interest on your principal of £400. It’s great to see how your savings grow!