Compound interest

Understanding Compound Interest

• Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.
• It can be considered as interest on interest, and it makes a deposit or loan grow at a faster rate compared to simple interest.
• The rate of compound interest is typically expressed as an annual percentage rate (APR).

Calculating Compound Interest

• The formula for calculating compound interest is A = P(1 + r/n)^(nt).
  • Where A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • r is the annual interest rate (in decimal).
  • n is the number of times that interest is compounded per year.
  • t is the time, duration the money is invested or borrowed for, in years.
• The frequency of compounding can be annually, semi-annually, quarterly, or monthly.

Application of Compound Interest

• Understanding compound interest is crucial in personal finance management. It is applicable in savings accounts, loans, mortgages, and investments.
• Compound interest allows your savings to grow faster because interest is calculated on the accumulated interest over time.

Example of Compound Interest Calculation

• If £1,000 is deposited in a savings account with an annual interest rate 5% compounded annually and left for 3 years.
• Using the formula, A = £1,000(1 + 0.05/1)^(1*3), calculate the result to find the final accumulated amount.

Key Points on Compound Interest

• Compound interest can significantly increase the value of an investment or loan over time.
• Understanding how compound interest works can help maximize savings on deposits or minimize the long term cost of loans.
• Be aware that for loans, compound interest can result in owing far more than the original sum borrowed, especially with high interest rates and long duration.