simple and compound interest- maths

• How is interest usually expressed?

  Interest is usually expressed as a percentage of the principal over a specific period, typically a year.
• If you save £100 in a bank account with a 5% interest rate, how much interest would you earn after one year?


  £5
• How much interest would you owe after borrowing £500 at an annual interest rate of 8% for one year?

  £40
• What is simple interest?

  Simple interest is calculated only on the principal amount, not on accumulated interest over time.
• What is the formula for calculating simple interest?


  $I =$$P \cdot r \cdot t$
• If you invest £1,000 at a 5% simple interest rate for 3 years, how much interest will you earn?


  £150
• How much total interest will you owe if you borrow £2,000 at a simple interest rate of 6% for 4 years?

  £480
• If you invest £500 at a simple interest rate of 4% for 5 years, how much interest will you earn?

  £100
• What is compound interest?

  Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods.
• What is the formula for calculating compound interest?

  $A =$$P \cdot (1 + r)^n$
• If you invest £1,000 at a 5% interest rate compounded annually for 3 years, what will be the final amount?

  $A \approx £1,157.63$
• If you invest £2,000 at a 4% interest rate compounded annually for 2 years, what will be the final amount?

  £2,163.20
• If you invest £1,500 at a 3% interest rate compounded annually for 3 years, what will be the final amount?

  £1,639.09
• What are the key differences between simple and compound interest?

  • Simple interest is calculated only on the principal amount.
  • Compound interest is calculated on the principal and accumulated interest.
  • Simple interest grows linearly, while compound interest grows exponentially.
  • Compound interest results in a higher final amount than simple interest for the same principal, rate, and time.
• If you invest £2,000 at 4% interest for 2 years, which method will give you more money, and how much more?

  Compound interest, £3.20 more
• What are some real-world applications of interest calculations?

  • Savings accounts use compound interest to grow savings.
  • Loans often use compound interest, increasing total repayment amounts.
  • Investments like stocks and bonds compound returns.
  • Credit cards charge compound interest on unpaid balances.
  • Retirement planning benefits from compound interest.
• If Sarah invests £5,000 today in an account that offers 3% compound interest annually, how much will she have in 5 years?


  £5,796.37
• What is the approximate amount you would have if you save £100 per month at age 25 with a 7% annual return by age 65?

  About £264,012.
• What is the approximate amount you would have if you start saving £100 per month at age 35 instead of age 25?

  About £122,709.
• Simple Interest Formula

  P × R × T
• Compound Interest Formula

  P × (1 + R)^T - P
• Simple Interest (SI) Formula

  P × R × T
• What is the Simple Interest on a principal amount of $5000 at a rate of 5% per annum for 2 years?

  P × R × T = $5000 × 0.05 × 2 = $500
• What is the Compound Interest on a principal amount of $10000 at a rate of 7% per annum for 3 years?

  P × (1 + R)^T - P = $10000 × (1 + 0.07)^3 - $10000 = $2433.99
• Simple Interest is calculated as a percentage of the principal amount. True or False?

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• Compound Interest is calculated only on the principal amount and not on any accrued interest. True or False?

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• If the interest rate is increased, the Simple Interest will also increase. True or False?

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  <front>If the interest rate is increased, the Simple Interest will also increase. True or False?</front>

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• Calculate the Simple Interest on a principal amount of $5000 at 4% interest for 2 years.

  $5000 × 0.04 × 2 = $400
• What is the Compound Interest on a principal amount of $10000 at 6% interest compounded annually for 3 years?

  $10000 × (1 + 0.06)^3 - $10000 = $1915.15
• If a deposit earns 5% annual interest, compounded quarterly, what is the interest earned in the first year?

  Using the formula: $10000 × (1 + 0.05/4)^(4*1) - $10000 = $251.25
• What is the Simple Interest on a loan of $20000 at 8% interest for 1 year?

  $20000 × 0.08 × 1 = $1600
• What is the Compound Interest on a principal amount of $5000 at 3% interest compounded monthly for 6 months?

  $5000 × (1 + 0.03/12)^(12*6/12) - $5000 = $67.95