Mathematics
Mathematics compound interest?
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Mathematics compound interest?
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Compound interest is the interest calculated on the principal amount and also on the accumulated interest of previous periods. It can be thought of as "interest on interest," making a sum grow at a faster rate than simple interest, which is calculated only on the principal amount.
Formula for Compound Interest:
- A = P (1 + r/n)^(nt)
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (as a decimal)
- n = the number of times that interest is compounded per year
- t = the number of years the money is invested or borrowed for
Example:
Suppose you invest $1,000 at an annual interest rate of 5% compounded annually for 10 years.
- P = $1,000
- r = 0.05
- n = 1
- t = 10
A = 1000 (1 + 0.05/1)^(1*10) = 1000 * (1.05)^10 ≈ $1,628.89
After 10 years, your investment would grow to approximately $1,628.89.
Key Concepts:
- Compounding Frequency: The more frequently interest is compounded (e.g., daily, monthly, quarterly), the faster the investment grows.
- Future Value: Compound interest helps in projecting the future value of an investment.