Simple &Compound Interest, Growth and Decay

• How many cards are in this collection?

  13
• Is simple interest based on the original amount or the current amount?

  Simple interest is based on the original amount.
• If you invest $500 over 3 years, how is simple interest calculated?

  It is calculated based only on the original $500.
• How do you calculate the final balance after simple interest has been earned on $300 at 4% for 6 years?

  The final balance is $372.
• What is the formula to calculate the final balance after simple interest?

  Final balance = Starting amount + (Starting amount × Rate × Time).
• How can you calculate the number of time periods over which simple interest is paid?

  By subtracting the original amount from the final amount and dividing by the product of the original amount and the rate.
• What is the formula to find the total interest earned in simple interest?

  Total interest = Final amount - Original amount.
• Is compound interest calculated based on the original amount or the current amount?

  Compound interest is calculated based on the current amount.
• How is compound interest calculated over time?

  It is calculated on the amount in the account at the end of each time period.
• What is the equation for the amount after n years with compound interest?

  The final amount is given by $A =$$P(1 + \frac{r}{100})^n$.
• Is compound interest the same as a repeated percentage increase?

  Yes, compound interest is the same as a repeated percentage increase.
• How can you calculate the final amount for an investment of £400 at 3% over 5 years using compound interest?

  The final amount can be calculated as $400 \times (1.03)^5$.
• Does the amount increase by the same value each year with compound interest?

  No, the amount does not increase by the same value each year.
• How do you calculate the original amount if given the final balance after compound interest?

  Divide the final balance by the compounded interest rate.
• If the final amount after 2 years at 5% is $771.75, what is the original investment?

  The original investment is $700.
• What is the definition of depreciation?

  Depreciation is where an item loses value over time.
• What is the equation for the value of an item after n years of depreciation?

  The value can be found by calculating $V =$$P(1 - \frac{r}{100})^n$.
• Is depreciation the same as a repeated percentage decrease?

  Yes, depreciation is the same as a repeated percentage decrease.
• How can you calculate the value of an item worth £200 that depreciates by 4% each year over 6 years?

  The value can be calculated as $200 \times (0.96)^6$.
• What is exponential growth?

  Exponential growth is when a quantity increases from an original amount by a percentage each year for n years.
• What is an example of exponential growth?

  Bacterial growth is an example of exponential growth.
• What is exponential decay?

  Exponential decay is when a quantity decreases from an original amount by a percentage each year for n years.
• What is an example of exponential decay?

  The temperature of hot water cooling down is an example of exponential decay.
• Can other time periods besides years be used for exponential growth or decay?

  Yes, other time periods such as seconds, hours, or days can be used.
• What are the key differences between simple interest and compound interest?

  • Simple interest is based on the original amount.
  • Compound interest is based on the current amount.
  • Simple interest is calculated only on the principal.
  • Compound interest is calculated on the principal plus accumulated interest.
• What are the steps to calculate the final balance after simple interest?

  1. Find the percentage of the starting amount using the rate.
  2. Multiply this by the number of time periods (years).
  3. Add this to the starting amount.
• What are the steps to calculate the original amount from the final balance after compound interest?

  1. Divide the final balance by the compounded interest rate.
  2. Use the formula: $Final Amount =$$P(1 + \frac{r}{100})^n$.
  3. Solve for P.
• What are the characteristics of depreciation?

  • Depreciation is a decrease in value over time.
  • It is calculated as a repeated percentage decrease.
  • The formula for depreciation is $V =$$P(1 - \frac{r}{100})^n$.
• What are the characteristics of exponential growth and decay?

  • Exponential growth increases by a percentage each year.
  • Exponential decay decreases by a percentage each year.
  • Both can occur over various time periods (seconds, hours, days, etc.).