compound interest - maths

• What is the main difference between simple interest and compound interest?


  Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal and accumulated interest.
• How is simple interest calculated on £100 at 10% for 2 years?


  Simple interest is calculated as £100 * 10% * 2 = £20.
• How is compound interest calculated on £100 at 10% for 2 years?


  Compound interest is calculated as follows: Year 1: £100 * 10% = £10, Total: £110; Year 2: £110 * 10% = £11, Total: £121.
• How can simple interest be explained in everyday terms?


  • Simple interest is like getting a fixed amount of pocket money.
  • Example: £5 every week for 4 weeks results in £20 extra.
• How can compound interest be explained in everyday terms?


  • Compound interest is like a snowball rolling down a hill.
  • It starts small but grows larger as it collects more snow.
• If you put £100 in a savings account with 10% interest, which type of interest would give you more money after 3 years?


  Compound interest would give you more money than simple interest after 3 years.
• What is the compound interest formula?


  The compound interest formula is $A =$$P \cdot (1 + r)^n$.
• In the compound interest formula, what does A represent?


  A represents the final amount after a certain period of time.
• In the compound interest formula, what does P represent?


  P represents the principal (initial investment).
• In the compound interest formula, what does r represent?

  r represents the annual interest rate (in decimal form).
• In the compound interest formula, what does n represent?

  n represents the number of years.
• If you invest £100 at 5% interest for 3 years, what is the final amount?


  The final amount is $A =$$100(1 + 0.05)^3 =$$£115.76$.
• What are compounding periods in relation to compound interest?


  Compounding periods refer to how often interest is calculated and added to the principal.
• What is the formula for compound interest with different compounding periods?


  The formula is $A =$$P \cdot \left(1 + \frac{r}{m}\right)^{m \cdot n}$.
• If £1000 is invested at 6% interest, compounded quarterly for 2 years, what is the final amount?


  The final amount is $A =$$1000 \cdot \left(1 + \frac{0.06}{4}\right)^{4 \cdot 2} =$$£1124.86$.
• How much more money would you have after 1 year if £500 is compounded monthly instead of annually at 4%?


  You would have £0.33 more with monthly compounding.
• What is the effect of time on compound interest?

  The longer the investment period, the more dramatic the effect of compound interest becomes.
• What are the positive applications of compound interest?


  1. Savings accounts: Money grows over time.
  2. Investments: Returns are reinvested for higher growth.
  3. Retirement funds: Long-term growth increases pensions.
• What are the negative applications of compound interest?


  1. Credit card debt: Interest compounds on unpaid balances.
  2. Loans: Unpaid amounts can increase due to compounding interest.
• What is simple interest?


  Simple interest is a method of calculating interest based only on the principal amount.
• What are the main components of simple interest calculations?

  • Principal (P): The initial amount of money borrowed or invested.
  • Rate (R): The interest rate, usually expressed as a percentage per year.
  • Time (T): The duration of the loan or investment, typically in years.
• What is the formula for calculating simple interest?


  The formula is $I =$$P \cdot R \cdot T$.
• Compare simple interest and compound interest.


  **Simple Interest**:

  • Calculated only on the principal amount.
  • Interest remains the same each year.
  • Formula: $I =$$P \cdot R \cdot T$.

  
  

  **Compound Interest**:

  • Calculated on the principal and accumulated interest.
  • Interest grows over time.
  • Formula: $A =$$P \times (1 + r)^t$.
• How does the interest earned in compound interest differ from simple interest over time?


  Compound interest increases because it is calculated on the principal plus accumulated interest.